• (i) The mean and variance of a Poisson random variable are equal. • (ii) For a standard normal random variable, the mean is zero…

Three fair coins are tossed independently. T is the event that two or more tosses result in heads. S is the event that two or more…

A fair six-sided die (with faces numbered 1, 2, 3, 4, 5, 6) is repeatedly thrown independently. What is the expected number of tim…

Let \(X\) be uniformly distributed on \([1,3]\), and let \(Y\) be uniformly distributed on \([2,4]\). If \(X\) and \(Y\) are indep…

Let \(X\) be exponentially distributed with parameter \(\lambda>0\), with density \[ f_X(x)=\begin{cases}\lambda e^{-\lambda x},&…

Consider two events \(T\) and \(S\), and let \(\overline{T}\) denote the complement of \(T\). It is given that \[ P(\overline{T})…