ICA \( 3[40 \) marks] Question 1 Mr. Ferguson recently retired from Botswana Power Corporation where he had been working for 20 years and as asked you to help him identify investment opportunities in the domestic market. Below is the state of the economy with the potential assets to be invested in, asset Zonke and asset Conke. NB: The returns are already converted from the percentages. \begin{tabular}{|l|l|l|} \hline State of the Economy & Return on Zonke & Return on Conke \\ \hline Depression & -0.20 & 0.05 \\ \hline Recession & 0.10 & 0.20 \\ \hline Normal & 0.30 & -0.12 \\ \hline Boom & 0.50 & 0.09 \\ \hline \end{tabular} Calculate:
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- Depression: Zonke = -0.20, Conke = 0.05 - Recession: Zonke = 0.10, Conke = 0.20 - Normal: Zonke = 0.30, Conke = -0.12 - Boom: Zonke = 0.50, Conke = 0.09 Show more…
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As noted in Definition 5.4 on page 220, the mean of a random variable is also called its expected value. This terminology is especially useful in gambling, decision theory, and the insurance industry. 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. $$\begin{array}{|l|c|c|} \hline {\text { Next year's economy }} \\ \hline & \text { Strong } & \text { Weak } \\ \hline \begin{array}{l} \text { Certificate } \\ \text { of deposit } \end{array} & 6,000 & 6,000 \\ \hline \begin{array}{l} \text { Office } \\ \text { complex } \end{array} & 15,000 & 5,000 \\ \hline \begin{array}{l} \text { Land } \\ \text { speculation } \end{array} & 33,000 & -17,000 \\ \hline \begin{array}{l} \text { Technical } \\ \text { school } \end{array} & 5,500 & 10,000 \\ \hline \end{array}$$ 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.
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