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An investor plans to put $50,000 in one of four investments. The return on each investment depends on whether next year’s economy is strong or weak. T

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asked 2021-07-02
An investor plans to put $50,000 in one of four investments. The return on each investment depends on whether next year’s economy is strong or weak. The following table summarizes the possible payoffs, in dollars, for the four investments.
Certificate of deposit
Office complex
Land speculation
Technical school
amp; Strong amp;6,000 amp;15,000 amp;33,000 amp;5,500
amp; Weak amp;6,000 amp;5,000 amp;−17,000 amp;10,000
Let V, W, X, and Y denote the payoffs for the certificate of deposit, office complex, land speculation, and technical school, respectively. Then V, W, X, and Y are random variables. Assume that next year’s economy has a 40% chance of being strong and a 60% chance of being weak. a. Find the probability distribution of each random variable V, W, X, and Y. b. Determine the expected value of each random variable. c. Which investment has the best expected payoff? the worst? d. Which investment would you select? Explain.

Answers (1)

2021-07-03

a) \(v | 600\)
\(P(V=v) | 1\)
\(w | 15000\ 5000\)
\(P(W=w) | 0.40 0.60\)
\(x | 33000 -17000\)
\(P(X=x) | 0.40 0.60\)
\(y | 5500\ 10000\)
\(P(Y=y) | 0.40 0.60\)
b) 6000, 9000, 3000, 8200
c) Office complex W, Land speculation X
d) Investment of office complex W

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