List of top Statistics Questions on Probability and Binomial Distribution

Let $X_{1}, X_{2}, \dots$ be independent variables each taking values $+1$ or $-1$ with equal probability respectively. If $S_{n}=\sum_{i=1}^{n} i X_{i}$ then $\lim_{n \rightarrow \infty} P\left(S_{n} < \sqrt{\frac{n(n+1)(2 n+1)}{3}}\right)$ where $\Phi$ is distribution function of standard normal variate, is

The variance of random variable $X$ having density $f_{X}(x)=ce^{-|x|}, -\infty<x<\infty$ is

Let $X_{1}$ and $X_{2}$ be i.i.
D. Bernoulli (p), $0