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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$E(XY)$ for a truncated bivariate normal
If $(X, Y)$ follows a bivariate Gaussian distribution with mean ${\bf \mu}$ and covariance ${\bf \Sigma}$ with truncation bounds $(a_x, b_x, a_y, b_y)$, can we compute $E(XY)$ in closed form? If not, ...
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Expected average distance in greedy matching on a circle
Now we have several independent and identically distributed random variables following the uniform distribution on the interval [0, 1].They are denoted as $x_1, x_2, x_3, ..., x_m$ and $y_1, y_2, ..., ...
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Scaling the conditioned random variable does not change conditional distribution, why?
Given two random variables $X$ and $Y$, I know intuitively that
$$
\mathbb{E}[X\,|\,Y]=\mathbb{E}[X\,|\,cY],
$$
where $c$ is some non-random constant. My intuition tells me that scaling the ...
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Expectation of Mahalanobis Distance and its logarithm
Suppose:
\begin{equation}
X \sim \mathcal{N}(X, \mu, \Sigma_x) \text{ st. } \Sigma_x \sim \mathcal{IW}(\Sigma_x; \Psi, v)
\end{equation}
Where $\mathcal{IW}$ is the Inverse-Wishart distribution. This ...
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Describing guaranteed profit situations which are stronger than just 'superfair wager'
Context.
I am tutoring a final year secondary school student in mathematics. To illustrate the principles of card-counting in a situation of sampling without replacement, I've decided to show her a ...
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Expected value of the square root of a lognormal variable
Let $X$ be a positive, lognormal random variable with known mean $\mu_X$ and variance $\sigma_X^2$. Since $X$ is a lognormal random variable, I know its pdf and moment-generating function (mgf).
pdf:
$...
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Question on the proof step in the theorem 1 of the Gap statistic paper
From the Gap statistic paper, during the proof for the theorem 1, we can see the below equality (p. 422),
$\begin{aligned} \operatorname{var}(X) & =\frac{1}{2} \int_{-\infty}^{\infty} \int_{-\...
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When the expected value of the gradient of function is equal to the expected value of the function multiplied by the gradient itself?
I'm having doubts on the conditions of an equality. Considering $f(X,w): \mathbb{R}^n \xrightarrow{} \mathbb{R}^n$ a function of n-variate random variable $X$ with an unknown distribution $p(x)$ and $...
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Gambling in multiple rounds with a maximum permitted bankroll and favorable or unfavourable probabilities
This is based on a deleted question, with the premises clarified to my understanding.
You are gambling in a casino with particular rules:
Bets are paid off at even amounts, so if you win a round you ...
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Calculating Expectation using the Linearity of Expectation law and sum of indicator random variables
I'm attempting to complete the problem sets for the Stanford CS109 Statistics course from 2021 as I follow along with the lectures.
I'm stuck on a particular problem in one of these problem sets. I ...
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Expectation and variance of bivariate skew normal distribution
I am fitting a bivariate skew normal distribution to a 2D data through the sn package in R. I get a $2 \times 1$ vector of ...
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Guessing the size of a set based on number of repeated random draws
I am trying to study a problem in algebraic number theory through a set of computational experiments. I have an enormous (say, of size $X$) family $\mathcal{F}$ of polynomials and I'm trying to ...
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Mean Squared Error for point estimation
I am attempting to understand Mean Squared Error when evaluating point estimators for particular parameters of interest. The book we are reading for class states the following:
The mean squared error (...
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Interpretation of expected wealth in Kelly betting paper
This is a sub-question of another StackOverflow question.
Kelly betting on horse races with uncertainty
in probability estimates (Metel 2017) describes an "ECC" variant of the Kelly method ...
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Using Law of iterated expectations, I want to calculate mean of Y, E(Y)
I obtain insights into calculating the conditional mean and
variance of Y given X, denoted as E(Y|X) and Var(Y|X) respectively. Building upon this
knowledge, I want to answer the follow-up question ...
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