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1d
answered $\sum_{k\ge 0} e^{-an} \frac{(an)^k}{k!}f(\frac{k}{n}) = \Bbb{E}\left(f\left(\dfrac{X_1+\cdots + X_n}{n}\right)\right)$
Jul
19
answered let $X$ be a standard Gaussian random variable. Show that $(X,X)$ is not absolutely continuous.
Jul
17
answered A basic question regarding the proof of existence of product measure
Jul
3
answered Show $\lim_{n\to\infty}\sqrt{n}\bigg(\frac{\sum_{j=1}^{n}X_j}{\sum_{j=1}^{n}X_j^2}\bigg)=Z$
Jul
3
answered What does the decomposition, weak union and contraction rule mean for conditional probability?
Jun
30
answered Integral change that I don't understand
Jun
30
answered Joint distribution of independent random variables
Jun
30
answered Convergence in probability of a random variable
Jun
26
answered Evaluating an expectation of the supremum of collection of random variables
Jun
26
answered $\sigma$-algebra generated by a set
Jun
26
answered $X $ and $Y$ are continuous $RVs$, such that$ f(x,y) = 2, 0\leq x\leq 1, 0\leq y\leq 1, 0\leq x+y\leq 1$
Jun
25
answered Trying to prove lim inf $(A_n) \subseteq$ lim sup $(A_n)$
Jun
25
answered The solution set of an inequality
Jun
24
answered Correlation coefficient of i.i.d variables
Jun
23
answered Confused how to calculate continous random variable with pdf that has a min
Jun
23
answered Measures in conditional expectation.
Jun
22
answered Probability of a uniform distrubated stochastic variable larger than another
Jun
20
answered How do you prove that if $ X_t \sim^{iid} (0,1) $, then $ E(X_t^{2}X_{t-j}^{2}) = E(X_t^{2})E(X_{t-j}^{2})$?
Jun
12
answered Marginal pdf $f_2(y)$ is proportional to $g_2(y)$.
Jun
12
answered (measure theoretic probability)Does $X$ have a gamma distribution if $X=Z^2$ and $Z$ has a Gaussian distribution?