Probstat/week5 practice 1

Practice exercises

1. Consider a random variable Z that becomes 1 with probability 1/3, 0 with probability 1/3, and 1 with probability 1/3. Find E[Z], and Var(Z).

Theoretical exercises

1. For a random variable X with variance Var(X). For a constant a, prove that $Var(aX)=a^{2}Var(X)$.

2. For a non-negative discrete random variable $X$ that takes on values 0,1,2,..., show that $\mathrm {E} [X]=\sum _{i=0}^{\infty }P\{X\geq i\}$.