A project with initial cost of $100$ offers the following payoffs at particular probabilities.

$\backslash$table$[[$Probability$,$Payoff$],[0\mathrm{.}1,400],[0\mathrm{.}5,150],[0\mathrm{.}4,0]]$

$($a$)$ What is the expected payoff for this project?

$($b$)$ What is the net profit expected on this project?

$($c$)$ What is the expected rate of return on this project?

$($d$)$ Calculate the variance and the standard deviation for this project.