e$)$ For the remaining parts of the problem, assume that P$3=50.$ Compute the state

price vector. Is the state price vector unique?

$($f$)$ Compute the stochastic discount factor.

$($g$)$ Suppose that a fourth security is introduced that pays $200$ in a recession, $100$ in

normal times, and $0$ in a boom. What is the no$-$arbitrage price of Security $4?$

$1$