Sem.1 Final

\( \DeclareMathOperator{\Normal}{\operatorname{Normal}} \DeclareMathOperator{\Exp}{\operatorname{Exp}} \)

Part I

Givens:

\begin{gather*} X \sim \Normal(\mu=2, \sigma^2 = 5) \\ W \sim \Exp(λ=-0.6) \end{gather*}

1. Produce good estimates (or exact values) for \(E[X]\) , \(E[W]\) , and \(E[Y]\) . Explain the method(s) you used in a few words or sentences.

2. Find the variance of Y.