New posts in Independence

Prove that for independent random variables $X_i$, we have $f_i(X_i)$ are independent.

Why are the random variables $X+Y$ and $X-Y$ independent when $X$ and $Y$ are i.i.d $N(0,1)$?

Probability Proof. $P(A | B) = P(A | B^c)$

If $Y\sim\mu$ with probability $p$ and $Y\sim\kappa(X,\;\cdot\;)$ otherwise, what's the conditional distribution of $Y$ given $X$?

How to show $\{u_1,\sum_i^2{u_i},\cdots,\sum_i^n{u_i}\}$ is linearly independent if $\{u_1,{u_2},\cdots,{u_n}\}$?

Is it true that $\lim_{n \to \infty} {(P(\forall i,j\leq n \text{ } [X_i, X_j] = e))}^{\frac{1}{n}} = P(X_1 \in Z(G))$?

Show that random variables $X$ and $Y$ are not independent, but nevertheless Cov$[X,Y] = 0$

Number of successes when the successes are positively correlated

Requirements on fields for determinants to bust dependence.

Factoring $1+x+\dots +x^n$ into a product of polynomials with positive coefficients