Expected value of f x Moments in maths are defined with a strikingly similar formula to that of expected values of transformations of random variables. Sep 28, 2017 · Stack Exchange Network. $\endgroup$ – Ele975. What is \(E[X]\)? Does the random variable have an equal chance of being above as below the expected value? First, we calculate the expected value using and the p. Commented Dec 20, 2020 at 1:50 $\begingroup$ So what's keeping you from clicking to Accept this fine answer (along with your thanks)? $\endgroup$ – BruceET. Dec 22, 2021 · Find expected value and variance of X, where X is the number obtained on the uppermost face when a fair die is thrown. Some of the properties of expected value are listed in Motivating Example 1 \(\PageIndex{1}\) Suppose for a certain college course, the grading policy is the following: Quiz Average - 15%; Exam 1 - 20% May 4, 2016 · Stack Exchange Network. Visit Stack Exchange Jun 12, 2020 · $\begingroup$ Thanks for the reply. Dec 20, 2022 · The expected value of a random variable X, denoted by E(X) or , measure where the Probability distribution is centered. probability; algorithms; expectation; Share. I understand untill the 2nd step. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. For a May 5, 2004 · X is a discrete random variable, then the expected value of X is precisely the mean of the corresponding data. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their Jan 3, 2025 · The expected value of a random variable is just the mean of the random variable. if it is deterministic then variance has to zero which intuitively suggests that it has to be an impulse Apr 10, 2022 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Nov 24, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Calculate the expected value and variance of the following continuous PDF: f(x) = 2x if 0<x< 1, 0 otherwise. If X is discrete, then the expectation of g(X) is defined as, then E[g(X)] = X x∈X g(x)f(x), where f is the probability mass function of X and X is the support of X. By definition, the expected value of the functiong( X,Y) = aX +bY of and Y is E(aX +bY) = x (ax +by)f(x,y)dxdy = x axf(x,y)dxdy Dec 17, 2015 · Is it still correct to refer to this construct as an expected value? please let me know. then you will get that result. Visit Stack Exchange Dec 3, 2018 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site. Visit Stack Exchange Apr 6, 2022 · $\begingroup$ @DavidParks: this question (the general one that is) has been addressed many times at MSE. 65 = 35 - 29. 2. In a related answer here we show a partial extension of the expectation rule. Visit Stack Exchange Nov 26, 2024 · The expected value of a discrete random variable X, symbolized as E(X), is often referred to as the long-term average or mean (symbolized as μ). I have given that $\mathbb{E}\left[ e^{X}\right]$ is finite and I am supposed to show that: $\int\limits_{\mathbb{R}}e^zP(X>z)dz$ is finite. Apr 9, 2022 · Example: Waiting for a train. In particular, if we toss a coin and define \(X\) to be the number of heads, then the expected value of \(X\) is the probability that the coin lands heads. ticket each time, making your expected net loss $4. kastatic. Also, the function f(x) may be defined such that f(x) is 0 outside a finite interval in which case the expectation is calculated within the finite range [lb, 10/3/11 1 MATH 3342 SECTION 4. If the bounds lb and ub correspond to the support of the distribution, e. The result suggests you should take the bet. To find the variance, first determine the expected value for a discrete uniform distribution using the following equation: The variance can then be computed Feb 17, 2018 · Moments. The expected value of this bet is $5. e. Visit Stack Exchange Jan 9, 2025 · If you're seeing this message, it means we're having trouble loading external resources on our website. 272 1 1 silver badge 13 13 bronze badges $\endgroup$ Add a comment | 2 Answers Sorted by: Reset to default Oct 20, 2018 · Hi im trying to understand conditional expectation and conditional probability based on sigma algebras. Proof. Mar 22, 2019 · Suppose $X$ is a random variable with some distribution $p$ and we need to evaluate $\mathbb{E}[f(X)]$. Provide details and share your research! But avoid . The conditions above uniquely define \( \E(X \mid \mathscr G) \) up to equivalence. Flip a biased coin twice and let Xbe the number of heads. Understanding the expected value isn’t just a mathematical exercise—it offers a predictive lens through which we can forecast likely Nov 26, 2020 · 1. If you imagine Aug 24, 2024 · In particular, if we toss a coin and define \(X\) to be the number of heads, then the expected value of \(X\) is the probability that the coin lands heads. This is readily apparent when looking at a graph of the pdf in Figure 1 and Nov 24, 2014 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Aug 14, 2020 · Example 37. Apr 24, 2022 · The basic idea is that \( \E(X \mid \mathscr G) \) is the expected value of \( X \) given the information in the \( \sigma \)-algebra \( \mathscr G \). Visit Stack Exchange Mar 4, 2021 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Sep 7, 2017 · I have asked this in a general way here: Approximating the expected value and variance of the function of a (continuous univariate) random variable. Indeed, on the Wikipedia page, the definition is given as: In general, if X is a random variable defined on a probability space (Ω, Σ, P), then the expected value of X, denoted by E[X], is defined as the Lebesgue integral $$\operatorname{E} [X] = \int_\Omega X \, \mathrm{d}P = \int_\Omega May 29, 2024 · Then you can compute the expected value of disbelief and the expect value of belief by first creating a value function. First, looking at the formula in Definition 3. E(X 3) = Σx 3 * p(x). f(x) = { 12 Compute the probability P(1 < X < 8). Visit Stack Exchange Jun 18, 2019 · Expected value of exp(X) Ask Question Asked 5 years, 7 months ago. 8k points) probability distributions; class-12; 0 votes. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their Jan 20, 2020 · Find the expected value, variance, standard deviation of an exponential random variable by proving a recurring relation. If you're behind a web filter, please make sure that the domains *. ". Asking for help, clarification, or responding to other answers. In all the figures above, note the red triangle marking the expected 2 days ago · The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences Jan 19, 2015 · The expected value is used to define the bias of f-hat in order to measure the average difference between the estimator and the true value. I have also read answers and coments to this question: Variance of powers of a random variable, but I think it refers to integer powers, which is not my case. 2 Cumulative Distribution Functions and Expected Values The Cumulative Distribution Function (cdf) ! The cumulative distribution function F(x) for a continuous RV X is defined for every number x by: For each x, F(x) is the area under the density curve to the left of x. Therefore an answer in that flavour would be most useful. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their 1 day ago · Statisticians denote it as E(X), where E is “expected value,” and X is the random variable. 1). I tried applying Apr 8, 2021 · I started with the following exponential distribution: $$ f_{exp}(x;\lambda) = \lambda\, e^{-x\lambda} \quad \forall\, x \in \mathbb{R}^+ $$ I know from internal courseslides and wikipedia that the Expected value of (continous) exponential distribution proof/derivation. Visit Stack Exchange Dec 20, 2020 · Yes I know that 𝜇 is the mean or the expected value and 𝜎^2 is the variance. Where an actual complete answer is really only one Jan 12, 2025 · which is also called mean value or expected value. Definition : Let X be a discrete random variable having a probability mass Function f(x). Visit Stack Exchange Nov 24, 2024 · Stack Exchange Network. 0. pdf(x) distribution. 2 (Expected Value and Median of the Exponential Distribution) Let \(X\) be an \(\text{Exponential}(\lambda)\) random variable. where: Σ: A symbol that means “summation”; x: The value of the random variable; p(x):The Nov 17, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site May 19, 2018 · Stack Exchange Network. Sobi. We start with two of the most important: every type of expected value must satisfy two critical properties: linearity and monotonicity. 5)/2, so its reciprocal of expectation is 0. Expected Value and Variance. Apr 25, 2016 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Nov 9, 2019 · If Xand Y are discrete, the conditional expected value of Y given Xis E(YjX= x) = X y yp YjX (yjx) If Xand Y are continuous, E(YjX= x) = Z 1 1 yf YjX (yjx)dy 25/31. Assume that this train is running on time. The symbol indicates summation over all the elements of the support . Please help. Follow edited Dec 17, 2015 at 22:31. In the context of probability theory, we can only take expected values of random variables, which we typically denote with uppercase letters, instead of lowercase letters—which we use for what are called deterministic Nov 29, 2022 · For a random variable, denoted as X, you can use the following formula to calculate the expected value of X 2:. Visit Stack Exchange Nov 21, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Sep 17, 2015 · I've previously asked the question on Stats SE, but I guess it fits the Math SE better. Commented Dec 20, 2020 at 2:47 Nov 19, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Mar 9, 2017 · When I tried to complete the above question, I obtained a value of 10 for the expected value and 0. asked Feb 14, 2014 at 18:03. distributions; variance; Sep 11, 2020 · The expression $$\mathbb E[g(x;y;\theta;h(x,z),)]$$ always means "the expected value with respect to the joint distribution of all things having a non-degenerate distribution inside the brackets. Modified 5 years, 7 months ago. The identity Eg(X) = X x g(x)f X(x) (2) is the most frequent method used to compute expectation of discrete random variables. So why is the solution of the integral not -1/2*exp(-4x)?. d. Jul 19, 2012 · Stack Exchange Network. An exercise in Probability. Expected value is a measure of central tendency; Jan 25, 2018 · The expected value of a function can be found by integrating the product of the function with the probability density function (PDF). If Then , the Sep 27, 2020 · While the "Darth Vader rule" (a silly name) applies to any non-negative random variable, I am going to simplify the analysis by looking only at continuous random variables. For a single discrete variable, it is defined by <f(x)>=sum_(x)f(x)P(x), (1) where P(x) is the probability density function. Example Bernoulli random variable = f0;1g f(x) = ˆ p if x = 1 1 p if x = 0 where 0 p 1 Jun 13, 2019 · Generally speaking, the expected value of an integral is an iterated integral, and so the normal mathematical rules for interchange of integrals apply. probability; 3 days ago · There must be something I am not understanding about the properties of expected values? probability; expected-value; Share. 1 \nonumber\] Use \(\mu\) to complete the table. Visit Stack Exchange Jul 10, 2015 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Sep 17, 2024 · Now for given N we need to find expected value of f(N). user107224. Visit Stack Exchange Nov 28, 2024 · Stack Exchange Network. Modified 3 years, 9 months ago. Sep 4, 2020 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Sep 3, 2023 · Formally, the expected value is the Lebesgue integral of , and can be approximated to any degree of accuracy by positive simple random variables whose Lebesgue integral is positive. Again we focus on the expected value of functions applied to the pair \((X, Y)\), since expected value is defined for a single quantity. In the section on additional properties, we showed how these definitions can be unified, by first defining expected value for nonnegative random variables in terms of the right-tail distribution function. E(X)= Var(X) = Check Consider a continuous random variable X that has the probability density function AO if 0 5 x 54 if 4 < x < 00, 5x otherwise. Where f(x) is the probability density function, which represents a function for the density curve. Follow edited Jun 10, 2017 at 16:58. Find May 3, 2016 · Stack Exchange Network. Sep 3, 2023 · Expected value: inuition, definition, explanations, examples, exercises. For many basic properties of ordinary expected value, there are analogous results for conditional expected value. Thus, the expected value of the uniform\([a,b]\) distribution is given by the average of the parameters \(a\) and \(b\), or the midpoint of the interval \([a,b]\). Extension to discrete and mixed random variables should also be possible, but I will not pursue that here. 期望值（Expected Value，EV） 笔记来源：StatQuest系列：Expected Values, Main Ideas!!! 1. Follow edited Mar 28, 2017 at 1:14. For the table below, we have grouped the outcomes ! that have a common value x =3,2,1 or 0 for X(!). We will prove it for the case when X and Y are continuous with joint pdf f(x,y). Then, to compute the expected value of X and X2 we construct a table to prepare to use (2 Nov 24, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Jul 3, 2017 · Stack Exchange Network. 1, the result Nov 26, 2016 · How to prove this $\text{E}( g(X) \mid X) = g(X)$ Self-study questions (including textbook exercises, old exam papers, and homework) that seek to understand the concepts are welcome, but those that demand a solution need to indicate clearly at what step help or advice are needed. The proof for the discrete case is similar. Responses on whether a very short answer was okay were somewhat mixed. Below, for argument sake we are somewhat randomly assign a value of one million to disbelief if a Jan 1, 2025 · Stack Exchange Network. If you imagine the probability histogram to be a thin lamina - like a thin sheet of metal cut in the shape of the Nov 16, 2024 · Another approach if you are happy with a numerical estimate (as opposed to the theorectical exact value) is to generate a bunch of data from the distribution, do the transformation, then take the mean of the transformed data as the estimate of the expected value. 6321 as the probability that the random variable is less than the expected value. E(X 2) = Σx 2 * p(x). Let \(X\) be a real-valued random variable with density function \(f(x)\). Oct 13, 2015 · Since you want to learn methods for computing expectations, and you wish to know some simple ways, you will enjoy using the moment generating function (mgf) $$\phi(t) = E[e^{tX}]. May 17, 2021 · Edit: I think a careful answer to your question needs to address the following point. where F (x) is the distribution function of X. For example, let X = the number of heads you get when you toss three fair coins. Properties of Jan 3, 2025 · The expected value of a random variable is just the mean of the random variable. In particular, usually summations are replaced by integrals and PMFs are replaced by PDFs. To see this more clearly, we first note that the expectation operator is an Sep 8, 2017 · Stack Exchange Network. The expected value \(\mu=E(X)\) is defined by \[\mu=E(X)=\int_{-\infty Add the values in the third column of the table to find the expected value of \(X\): \[\mu = \text{Expected Value} = \dfrac{105}{50} = 2. I tried calculating but I find the expected value integral 5 days ago · The expectation value of a function f(x) in a variable x is denoted <f(x)> or E{f(x)}. 1), EX, the expected value of X is the sum of the values in column F. 50 per ticket). \] In fact, moments are especially useful in the context of random variables: recalling that \(\text{Var}(X) = Sep 9, 2023 · This means if you play many, many times, on average, you’d expect to gain 50 cents per play (though you’re paying $5 for the. Once you start putting subscripts in $\mathbb E$ then you specify perhaps a "narrower" joint distribution for which you want (for your reasons), to average over. The expectation operator has inherits its Oct 22, 2024 · For a continuous random variable, the expected value is calculated using an integral: E (X) = \int_ {-\infty}^ {\infty} x f (x) \, dx E(X) =∫ −∞∞ xf (x)dx. The expected value and variance are two statistics that are frequently computed. A quick search for Fun ini's theorem plus distribution will show you some instances. When you assume a pdf for an RV(taking infinite values) the density function is spread asymptotically. user940 asked Jan 31, 2015 at 16:58. Suppose that you have a standard six-sided (fair) die, and you let a variable \(X\) represent the value rolled. The expected value is a number that summarizes a typical, middle, We now look at taking the expectation of jointly distributed discrete random variables. Specifically, for a discrete random variable, the expected value is computed by "weighting'', or multiplying, each value of the random variable, \(x_i\), by the probability that Jun 10, 2023 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Jul 31, 2023 · One way to determine the expected value of \(\phi(X)\) is to first determine the distribution function of this random variable, and then use the definition of expectation. Visit Stack Exchange Feb 4, 2017 · Stack Exchange Network. If you repeat this experiment (toss 3 days ago · By inspection we can see that in the first calculation the uniform has expected value (2. We can use the probability distribution table to compute the expected value by multiplying each outcome by the probability of that outcome, then adding up the Feb 9, 2022 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Mar 9, 2018 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site May 18, 2022 · Stack Exchange Network. Mar 23, 2016 · Stack Exchange Network. asked Dec 22, 2021 in Probability Distribution by Riyamishra (25. For help writing a good self-study question, please visit the meta pages. 1. Consider a given Mar 16, 2017 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their Jan 11, 2025 · where ub and lb are arguments and x has the dist. May 4, 2016 · Stack Exchange Network. where: Σ: A symbol that means “summation”; x: The value of the random variable; p(x):The Apr 24, 2022 · We say that we are computing the expected value of \(Y\) by conditioning on \(X\). 1 离散型事件的期望值 从一场打赌开始，下图左侧小人儿和我打赌，在小岛StatLand上随机采访岛上某一个居民，如果该居民听说过电影Troll2，那么我输给小人儿1dollar，如果该居民没有听说过，那么我赢得1dollar 我们统计一下 Nov 24, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site In probability theory, an expected value is the theoretical mean value of a numerical experiment over many repetitions of the experiment. The mean is the center of the probability distribution of \(X\) in a special sense. If you play many games in which the expected value is positive, the gains will outweigh the costs in the long run. org are unblocked. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their Jun 9, 2017 · What is the expected value of $1/x$? That is, what is the value of: $$\langle1/x\rangle = \int_0^1 \frac{f(x)}{x} \mathrm d x$$ probability; expected-value; beta-distribution; moment-generating-function; Share. of the exponential distribution . 1. Viewed 2k times 1 $\begingroup$ $\newcommand{\E}{\mathbb{E}}\newcommand{\Var}{\operatorname{Var}}$ In An Introduction To Statistical Learning page 19, it states. 8, and some simple algebra establishes that the reciprocal has expected value $\frac23\log 4 Aug 1, 2015 · The expected value or mean of a random variable g(X) is E[g(X)]= 8 >< >: Z ¥ ¥ g(x)fX(x)dx if X has pdf fX å x g(x)fX(x) if X has pmf fX provided that the integral or the sum exists (is finite); otherwise we say that the expected value of g(X) does not exist. 75. We need to be clear about what "taking expected value" means. One might wonder why the function that gives the probabilities of the various outcomes associated with a random variable is called a "probability mass function". Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The variance should be regarded as (something like) the average of Apr 24, 2022 · The expected value of \(X\) is also called the mean of the distribution of \(X\) and is frequently denoted \(\mu\). Follow edited Sep 21, 2018 at 9:33. Improve this question. [-inf, inf] in the default case, then the integral is the unrestricted expectation of f(x). 4. CC-BY-SA 4. For example, if then The Explore math with our beautiful, free online graphing calculator. You can calculate the EV of a continuous random variable using this formula: Expected value Expected value. The \(n\) th moment of a real-valued function \(f\) about point \(c\) is given by: \[ \int_\mathbb{R} (x - c)^n f(x) dx. In probability and statistics, the expected value is the theoretical mean (this assumes that the experiment is run a relatively large number of times) of a random variable, X. Cite. Visit Stack Exchange The expected value of a random variable has many interpretations. Nov 28, 2024 · Basically what can go so wrong that an expected value does not exists? probability; probability-theory; expectation; Share. Basically the first page I show how I get the pdf and cdf for minimum and Mar 21, 2019 · Stack Exchange Network. We Feb 7, 2024 · Should you take the bet? You can use the expected value equation to answer the question: E(x) = 100 * 0. Viewed 111 times 1 $\begingroup$ I trying to prove that something is finite. kasandbox. In all the figures above, note the red triangle marking the expected value. About; Statistics; Number Theory; Java; Data Structures; Cornerstones; Calculus; Expected Value and Center of Mass. The expected value is related to the variance of a random Feb 13, 2020 · The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences Nov 16, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Nov 24, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Feb 16, 2014 · denote the number of heads. But I don't know what this tells me about the distribution, nor if I integrated correctly. The Sounder commuter train 69 from Lakeview to Seattle, Washington arrives at Tacoma station every 20 minutes during the morning rush hour. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their Nov 20, 2015 · Thanks for contributing an answer to Cross Validated! Please be sure to answer the question. Expected ValueVarianceCovariance Double Expectation: E(Y) = E[E(YjX)] Theorem A on page 149 To make sense of this, note While E(YjX= x) = R 1 1 yf Feb 21, 2016 · Stack Exchange Network. where p(x) is the proportion of observations taking the value x. 2/-4 = -1/2. 2,623 17 17 Nov 25, 2024 · Stack Exchange Network. Jun 26, 2022 · Stack Exchange Network. Hopefully this idea will become clearer during our study. csss csss. For a single continuous variable it is defined by, <f(x)>=intf(x)P(x)dx. You can calculate the EV of a continuous random variable using this formula: Expected value formula for continuous random variables. (2) The expectation value satisfies <ax+by> = a<x>+b<y> (3) <a> = a (4) <sumx> = sum<x>. From the definition of expectation in (8. The definition of expectation follows our intuition. Properties of Expected Value. That is why I marked it as duplicate. Jan 13, 2022 · The expectation of a discrete random variable X with probability mass function f is defined to be E(X) = X x:f(x)>0 xf(x) whenever this sum is absolutely convergent. expected-value; kullback-leibler; Share. At this point, it should not surprise you that the following theorem is similar to Theorem 5. Because expected values are defined for a single quantity, we will actually define the expected value of a combination of the pair of random variables, i. Here, $f(X)$ may or may not have the Jul 12, 2018 · $$F(X)=\frac{99}{1-X}\quad\text{and}\quad X\equiv Uniform[0,1]$$ What is the expected value of above distribution. This means that over the long term of doing an experiment over and over, you would expect this average. Aug 7, 2020 · Stack Exchange Network. This Nov 23, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site 5 days ago · In particular, if we toss a coin and define \(X\) to be the number of heads, then the expected value of \(X\) is the probability that the coin lands heads. 2,268 14 14 silver badges 27 27 bronze badges. org and *. Oct 21, 2022 · no matter X and Y are both discrete, both continuous, or one discrete and one continuous. The proof of this fact is a simple application of \[E(x)=x_{1} p_{1}+x_{2} p_{2}+x_{3} p_{3}+\ldots+x_{n} p_{n} \label{expectedvalue}\] The expected value is the average gain or loss of an event if the experiment is repeated many times. Sep 30, 2011 · where f X(x) = PfX= xgis the probability mass function for X. To compute the expected value EX, we can proceed as described in (8. May 16, 2019 · expected value for $(f(X) + \epsilon - \hat{f}(X))^2$ Ask Question Asked 5 years, 7 months ago. Definition 1 Let X be a random variable and g be any function. Therefore, also the Lebesgue integral of May 21, 2014 · Expected Value Expected Value of a function The expected value of a function of a random variable is de ned as follows Discrete Random Variable: E[f(X)] = X all x f(x)P(X = x) Continous Random Variable: E[f(X)] = Z all x f(x)P(X = x)dx Sta 111 (Colin Rundel) Lecture 6 May 21, 2014 2 / 33 Expected Value Properties of Expected Value Aug 1, 2023 · Definition: Term. 35 + (-45) * 0. Ask Question Asked 3 years, 9 months ago. 2,261 16 16 silver badges Oct 29, 2020 · Stack Exchange Network. Nov 27, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site May 9, 2018 · I am working on calculating the expectation and then variance of the range from a Uniform(-theta, theta) distribution, but have gotten stuck. $$ Sep 14, 2020 · I have found several past answers on stack exchange (Find expected value using CDF) which explains why the expected value of a random variable as such: $$ E(X)=\int_{0}^{\infty}(1−F_X(x))\,\mathrm dx $$ However, I am studying a partial-partial equilibrium in search theory where we have the following integral instead where a is a positive free May 18, 2020 · The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences; available under CC-BY-SA 4. Example 4. Visit Stack Exchange Nov 24, 2024 · Now what I don't understand with this: doesn't the result of the expected value E[f(x)] depends on the choice of the pdf? For example of you have a simple function such as f(x) = x (imagine the integration domain is [0,1]), if you choose a uniform pdf or a gaussian distribution, wouldn't the result of E[f(x)] be different? 5 days ago · The expectation value of a function f(x) in a variable x is denoted <f(x)> or E{f(x)}. Visit Stack Exchange Dec 9, 2015 · $\begingroup$ @Alexis that's the difficulty with this sort of question (I brought this up on meta in September) -- we're forced either to give an answer that's overly brief by the usual SE standard or to leave the question unanswered. The expectation is also called the mean value or the expected value of the random variable. f. kjetil b Nov 23, 2024 · Stack Exchange Network. F(x)=P(X≤x)=f(y)dy −∞ Nov 29, 2022 · For a random variable, denoted as X, you can use the following formula to calculate the expected value of X 3:. . Then the probability of rolling a 3, written as \(P(X = 3)\), is 1 6 , since there are six sides on the die and each one is equally likely to be rolled, and hence in particular the 3 has a one out of six chance of being rolled. zesy zesy. Jan 12, 2025 · For a continuous random variable, the expectation is sometimes written as, g(x) d F (x). user119249 user119249. 1 for computing expected value (Equation \ref{expvalue}), note that it is essentially a weighted average. 25 = 5. Dec 4, 2019 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Nov 21, 2024 · Expected value is $\sum{x_ip(x_i)}$ But this is where I get stuck, I'm really rusty on my statistics and I'm not sure exactly how to structure it in the next step? I think I want to get the form of the following out of the summation $\sum _{k=0}^{n} \binom{n}{k}p^k(1-p)^{n-k} = (p + 1 As we mentioned earlier, the theory of continuous random variables is very similar to the theory of discrete random variables. Jul 24, 2017 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site 5 days ago · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Oct 22, 2024 · If X ≤ Y for all possible values, then the expected value of X is less than or equal to the expected value of Y: X ≤ Y E(X) ≤ E(Y) This property shows that if one random variable is always smaller than another, its expected value will also be smaller. 1 answer. Is it possible to rigorously derive the formula for expected value of continuous random variable starting with expected variable in discrete case, i. There is nothing wrong with duplicates. Indeed, if we think of the distribution as a mass distribution (with total mass 1), Aug 1, 2024 · For a continuous random variable X with probability density function f(x), the expected value is defined as: E(X) = \int_{-\infty}^{\infty} x \cdot f(x) \, dx. Follow asked Sep 19, 2014 at 21:00. , we look at the expected value of a function applied to \((X,Y)\). What if I want to find the expected value of the PDF itself? Th Jan 17, 2023 · Probability . where f (x) is the Sep 30, 2011 · Thus, expected values for continuous random variables are determined by computing an integral. g. Any help would be greatly appreciated. Visit Stack Exchange Apr 23, 2022 · In the introductory section, we defined expected value separately for discrete, continuous, and mixed distributions, using density functions. How it it possible that the integral sign is still there in the final step? $\endgroup$ – Tim Feb 4, 2021 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Jun 13, 2013 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site Nov 22, 2024 · If you are interested further in this topic, there is a published paper by Nadarajah and Kotz that derives the pdf of max$(X,Y)$ as an Azzalini skew-Normal, and derives the expectation etc: Dec 8, 2018 · Here your pdf for the deterministic signal is an impulse of infinite amplitude and unit area. Nov 24, 2024 · Stack Exchange Network. For a single discrete variable, it is defined by <f(x)>=sum_(x)f(x)P(x), (1) where P(x) is the Aug 1, 2024 · For a continuous random variable X with probability density function f(x), the expected value is defined as: E(X) = \int_{-\infty}^{\infty} x \cdot f(x) \, dx. The fourth column of this table will provide the values you May 12, 2015 · At first reading, it looks like you are trying to "prove" a definition. jcwr bkiiwr ltpib hxxvq xjoela sltif mmaute hof egbdccg jdgry