Question

Suppose random variables Z, are exponentially distributed: Zi Exp(2) for i = 1,2,...,n and assume that the random variables 2; are independent. For the definition and properties of the exponential distribution, refer to the formula sheet from the second lecture. For each of the following functions of the Zi, find the expectation E[ ] and variance Var[ ]. (a) 3 21 -5 (b) 1.5 Z1 +2 22 - 3 (c) 1-32 (simplify as much as possible, but final answer will contain )