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Chapter 6: Q. 44 (page 379)

Rotter Partners is planning a major investment. The amount of profit X(in millions of dollars) is uncertain, but an estimate gives the following probability distribution:

Based on this estimate, μX=3and σX=2.52

Rotter Partners owes its lender a fee of $200,000plus 10%of the profits X. So the firm actually retains Y=0.9X-0.2from the investment. Find the mean and standard deviation of the amount Ythat the firm actually retains from the investment.

Short Answer

Expert verified

The mean and standard deviation are

μY=2.5million dollars

σY=2.268million dollars

Step by step solution

01

Given Information

Given in the question that

μX=3σX=2.52Y=0.9X−0.2

02

Explanation

Properties mean and standard deviation

μaX+b=aμX+b

σaX+b=aσX

Then we obtain for Y=0.9X-0.2

localid="1649908061806" μY=μ0.9X-0.2=0.9μX-0.2=0.9(3)-0.2=2.5

localid="1649908064829" σY=σ0.9X-0.2=0.9σX=0.9(2.52)=2.268

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