Question

An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $50,000. If the economy grows at a moderate pace, the investment will result in a profit of $20,000. However, if the economy goes into recession, the investment will result in a loss of $50,000. You contact an economist who believes there is a 30% probability the economy will remain strong, a 60% probability the economy will grow at a moderate pace, and a 10% probability the economy will slip into recession. What is the expected profit from this investment? The expected profit is $0 (Type an integer or a decimal.)

Answer 1

Suppose, random variable X denotes profit resulted in the investment.

Probability distribution of X is as follows.

X=x 50000 20000 -50000 Total P(X=x) 0.30 0.60 0.10 1.00

$\tiny \therefore E\left ( X \right )=\sum _x x*P\left ( X=x \right )=50000*0.30+20000*0.60-50000*0.10=22000$

Hence, expected profit is $ 22000.