Questions tagged [variance]

For questions regarding the variance of a random variable in probability, as well as the variance of a list or data in statistics.

1,181 questions
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The random size is distributed according to the normal law, which is an average of 15. Calculate this random size dispersion if it is known that the probability of gaining values ​​from the range [15; ...
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Proving expectation and variance of a function of a random variable tends to a fix point

Given $f:\mathcal{X} \rightarrow \mathbb{R}$ is a continuous function and $\mathbb{E}_{Q(X)}[X] \rightarrow x^\star$ ($x^\star$ is a fix number), $\mathbb{V}\text{ar}_{Q(X)}[X] \rightarrow 0$. How can ...
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Proving convergence of expectation and variance given Rényi's $\alpha$-divergence tends to 0

I denote $p, q$ as density function of $P, Q$. Given $Y, X$ are random variables and \begin{align} \int q(x)\mathbb{D}_{\alpha}[p(Y\mid X=x)\,||\,p(Y\mid x^\star)] \,dx \rightarrow 0 \end{align} ...
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Can Conditional Expected Value be negative in normal distribution?

So, the problem gives me this facts (for a Normal bivariate distribution X,Y) $$Var(Y|X=x) = 5$$ $$E(Y|X=x) = 2 + x$$ It asks me to find $$E[Y^2|X=7]$$ I tried this: using the conditional variance ...
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For a sequence of experiments where each $X$ is the number of trials until success with varying $p$, is each $X$ independent?

Assume that, every time you buy a box of Wheaties, you receive a picture of one of the $n$ baseball player. Let $X_k$ be the number of additional boxes you have to buy, after you have obtained $k-1$ ...
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Rao-Blackwell and Cramer-Rao LB comparison

Let $X_1, X_2, \dots, X_n$ be a random sample following the Geometric distribution. $$\prod\limits_{i=1}^{n} f(x_i|p) = (1-p)^{\sum\limits_{i=1}^n x_i-n}p^n$$ Since the pmf of the Geometric ...
Difficult demonstration - How to show that $H_n$ is normal distributed $N(\xi,\sigma^2)$ starting from its moments $ξ$ and $σ$?
I was thinking that if the function $H_n$ of cumulative distribution converges to a distribution $H$, then $\epsilon_n$ should converge to $\epsilon$ what could be expressed as follows: If $H_n$ is ...
The law of total variance: $$\text{Var}(X) = \mathbb{E}(\text{Var}(X\mid Y)) + \text{Var}(\mathbb{E}(X\mid Y)).$$ There is also something called the law of total covariance:  \text{Cov}(X,Y) = \...