91Ó°ÊÓ

The potential returns on the four investments are given as

Consider the payoffs for the certificate of deposit, office complex, land speculation, and technical school as V, W, X, and V, respectively. It is also assumed that the economy will be strong 40% of the time and weak 60% of the time next year.

The payoff probability distribution for the certificate of deposit is defined as follows:

The payoff probability distribution for the office complex is defined as follows:

The payoff probability distribution for land speculation is defined as follows:

The payoff probability distribution for technical school is defined as follows:

V's expected value can be calculated as

$$\begin{gathered} E\left(V\right)=\underset{}{∑}P(V=v) \\ E\left(V\right)=\left[\right(6000×0.40)+(6000×0.60\left)\right] \\ E\left(V\right)=(2400+3600) \\ E\left(V\right)=6000 \end{gathered}$$

W's expected value can be calculated as

$$\begin{gathered} E\left(W\right)=\underset{}{∑}P(W=w) \\ E\left(W\right)=\left[\right(15000×0.40)+(5000×0.60\left)\right] \\ E\left(W\right)=(6000+3000) \\ E\left(W\right)=9000 \end{gathered}$$

X's expected value can be calculated as

$$\begin{gathered} E\left(X\right)=\underset{}{∑}P(X=x) \\ E\left(X\right)=\left[\right(33000×0.40)+(-17000×0.60\left)\right] \\ E\left(X\right)=(13200-102000) \\ E\left(X\right)=3000 \end{gathered}$$

Y's expected value can be calculated:

$$\begin{gathered} E\left(Y\right)=\underset{}{∑}P(Y=y) \\ E\left(Y\right)=\left[\right(5500×0.40)+(-10000×0.60\left)\right] \\ E\left(Y\right)=(2200-6000) \\ E\left(Y\right)=8200 \end{gathered}$$

The expected values of the random variables V, W, X, and Y are as follows:

E(V) = 6000

E(W) = 9000

E(X) = 3000

E(Y) = 8200

The Office Complex investment has the best expected payoff, while the Land Speculation investment has the worst expected payoff.

The expected values of the random variables V, W, X, and Y are as follows:

E(V) = 6000

E(W) = 9000

E(X) = 3000

E(Y) = 8200

The Office Complex investment has the best expected payoff, while the Land Speculation investment has the worst expected payoff.

As a result, the Office Complex investment must be chosen.