Problem $3.$ Consider the following cash flows of a project with $N=2$ and $i=10\%.$

$($a$)$ Assuming that the cash flows are independent of each other, find the mean and the standard

deviation of the NPV of this project.

$($b$)$ Assuming that the cash flows have the following correlation coefficients, find the mean and the

standard deviation of the NPV$.$

${}_{01}=0\mathrm{.}30$;${}_{02}=0\mathrm{.}10$;${}_{12}=0\mathrm{.}50.$

$($c$)$ Assuming that the cash flows are perfectly positively correlated, find the mean and the standard

deviation of the NPV$.$