Show that if $X_1, X_2,...,X_{11}$ are random variables, and $\operatorname{corr}(X_i,X_j) = r$ for $ i\neq j$ , then show $r \geq -1/10$
38169
Bounds on off-diagonal entries of a correlation matrix
154945
$|px^2+qx+r|\le1$ for all $x$ in $[-1; 1]$, show that $|rx^2+qx+p|\le2$ for all $x$ in $[-1; 1]$
42451
Sum of two uniform random variables
101754
Transformation of Random Variable $Y = X^2$
77412
Product of $\min$ and $\max$ of $n$ i.i.d. random variables.
67313
Proving $\{(x_1, x_2) \in \mathbb{R}^2_{+} \mid x_1 x_2 \geq 1\}$ is convex
13723
Doubly stochastic matrix proof
152495
Prove that if $X$ and $Y$ are Normal and independent random variables, $X+Y$ and $X-Y$ are independent
9621
Bound for the correlation of three random variables
104847
Minimum covariance of 2 random variables given the covariance of each with a third random variable
31631
Proof Verification: Joint variance of the product of a random matrix with a random vector
129598
Linear transformation of random variables
68484
Revision of Borel-Cantelli, $(X_n)_{n \geq 1}$ sqn of $\geq 0$ identical RVs with $E(X) < \infty$ then $X_n/n \to 0$ a.s., are my arguments correct?
135446
Proof that the probability of one RV being larger than $n-1$ others is $\frac{1}{n}$
141165
Probability of $p(x_1<x_2<\max(x_3,x_4))$
34929
Prove ${M}\choose{N_1}$ ${M}\choose{N_2}$ $\leq$ ${2M}\choose{N_1+N_2}$ for $M, N_1, N_2 \in \mathbb{N},\,M\geq N_1,N_2$.
98662
$P(|X|\ge\lambda a)\ge (1-\lambda)^2a^2$ for $0\le \lambda \le 1$