With X being a continous random variable, what prove satisfies Var(X)≤1/4
4130
Variance of a bounded random variable
20291
Probability of random variables converging
157432
How to use the Mean Value Theorem to prove the following statement:
52380
How to prove the function $e^x$ is continous for all real numbers
61758
Limit question on independent random variables (Exercise 4.2.4 from Grimmett and Stirzaker)
28100
Prove I know a value $v$ in a Pedersen Commitment without revealing it
36374
Exercise 1.6.3 from Alon & Spencer's *The Probabilistic Method*: prove that $Pr[|X-Y| \leq 2] \leq 3 Pr[|X-Y| \leq 1]$ for i.i.d. real RVs $X$ and $Y$
136686
Find the almost sure limit of $X_n/n$, where each random variable $X_n$ has a Poisson distribution with parameter $n$
69715
Proving $\text{Var}{(\hat{y}_h)} = \sigma^2 \left(\frac{1}{n} + \frac{(x_h-\bar{x})^2}{S_{xx}}\right)$
1264
Find the probability of an event determined by an inequality on exponential random variables
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
118091
Taylor expansion of $\exp(-x)$: proof tail is positive
127486
Probability of continuous random variable
106868
Prove that $x+\frac1{4x} ≥ 1$ for $x>0$
88676
Proof verification : $X_n \to X$ in distribution, $Y_n \to 0$ in probability $\implies$ $X_nY_n \to 0$ in probability
62665
If X and Y are continuous random variables, then the random vector (X,Y) is a continuous random vector?
29679
Prove: $|x-y|\leq |x|+|y|$