Questions tagged [expected-value]
The expected value of a random variable is a weighted average of all possible values a random variable can take on, with the weights equal to the probability of taking on that value.
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Expected value of iid squared conditioned on sum
I would be interested in finding the value of the following expression:
$$\mathbb{E}[X_k^2\mid S_N]$$
where $X_k$ are iid random variables with $\mathbb{E}[X_k]=\mu$ and $\operatorname{Var}[X_k]=\...
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How is summation by parts technique used in this derivation?
In this answer, whuber comments that the technique used in the answer is summation by parts:
The discrete case, assume that $X \ge 0$ takes non-negative integer
values. Then we can write the ...
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Expected Value of Continuous Data in R
I am currently working with data involving three continuous variables in R, and I want to calculate the expected value of the joint probability distribution.
I attempted to use the ...
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Second moment of weighted average of random variables
I stumbled upon problem 254 from the SOA Exam P list in
https://www.soa.org/globalassets/assets/Files/Edu/edu-exam-p-sample-quest.pdf
for which I am puzzled by the solution described in
https://www....
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analytical asymptotic approximation of the expected maximum, mean, and minimum distance of nearest neighbours in unit ball
Say I uniformly at random distribute $x = n^3$ (independent identically distributed) points in a ball of radius $r=1$ in $\mathbb{R}^3$.
What can be said about the expected maximum, minimum, and mean ...
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how can predictive distributions be considered as expectations?
I guess that the prior and posterior predictive distributions can be considered expectation of $p(y|\theta )$ (in case of prior predictive distribution) and $p(\widetilde{y}|\theta )$ (in case of ...
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Expectation of binomial random variable
Having trouble understanding something I read in a paper recently.
Say we have $X \sim \operatorname{Binomial}(N,p).$ The paper states:
$$E[X \mid N,p] = Np$$ (so far so good)
and
$$E[X] = \mu p$$
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Convex predictive mean of Gaussian Process
In Gaussian process (GP) regression, predictive mean is
$$ K(X^*,X)[K(X,X)+\sigma^2I]^{-1} \textbf{y}$$
Is there a method to ensure that the predictive mean is convex with respect to the test input $X^...
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I don't think this is conditional dependence, so what is it?
I am looking for the name of the following phenomenon. There are three random variables, $X,Y,Z$. We have $P(X,Y) \neq P(X)P(Y)$ and $P(Y,Z) \neq P(Y)P(Z)$. In other words, $X$ and $Y$ are dependent, ...
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I would like some insight into what I have been working on here
I work in roofing sales which involves door-knocking at the entry level. Our daily numbers are printed in our GroupMe chat for our branch. I took it upon myself to do some analysis on those numbers. ...
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Expectation under convex order by multiplying
I am trying to understand if the following statement is true, or the conditions under it is satisfied. Let $M,N$ and $X>0$ be random variables. If the following inequality holds for any concave non-...
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Computing a Confidence Interval for E[X] when PMF is given
I am given a Probability Mass Function for a discrete random variable.
From the PMF I computed the Expected Value $E[X]$, the Variance $V[X]$ and the Standard Deviation $S[X]$.
Here is an example (the ...
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Expected Value Chi Square distribution
I'm trying to simulate the distribution from the sample variance $s^2$ and compare it with the theoretical distribution.
Therefore, I perform a fairly simple simulation (upfront, I'm not a ...
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Expectation under convex order
I am trying to understand if the following statement is true. Let $M,N$ and $X$ be random variables. If the following inequality holds for any concave non-decreasing function $u$
\begin{equation}
\...
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Distribution of outcomes of multiple binomial distributions
I have a sample of 50 subjects, where every subject completes a task with two possible outcomes (left or right hand use, with 50% probability) 30 times. On an individual level, this leads to a ...