3. Suppose $X$ has the pdf $$ f(x)=\left\{\begin{array}{cc) \frac{c}{\sqrt{x}} \exp (-x) & x>0 0 & \text { otherwise } \end{array} ight $$ where $c>0$. (a) Find $c$. (b) Find $E(X)$ and $\operatorname{Var}(X)$. (c) Find $E\left((\sqrt{X}-1)^{2} ight)$. (d) Compute $P(X>4)$. Do not leave your answer in terms of an unevaluated integral. SP.PC. 0821