ll Dut inus lt Bold out simply leaves rather than order something else. (Hint: F

Question

ll Dut inus lt Bold out simply leaves rather than order something else. (Hint: Find the probability distribution of the number of units sold and observe that revenue selling price times number of units sold.) 4. Suppose you borrow $1000 for one year at a variable interest rate tied to the yield on gov- ernment bonds. As a result, the total interest you will pay is a random variable Xi, having mean $60 and standard deviation $2. You invest the borrowed money. Your earnings on the investment, X2, have mean $85 and standard deviation $8. Suppose the correlation between your earnings and the interest you pay on the loan is 0.3. (a) Your net earnings at the end of the year are given by Y X Xi. Find the expected value of your net earnings (b) Find the standard deviation of ypur net earnings. 5. Let X, Y, and Z be random variables. Which one(s) of the following statements is/are true? (a) if Cov(x, Y) > Cov(Y, 2) then pxy>pyz

Explanation / Answer

The net earnigs is given by Y=X2-X1 There for eits expectaion is given by E(Y)=E(X2-X1)=E(X2)+E(X1)=85-60=24 to find the variance of net earnings var(Y)=Var(X2-X1)=Var(X2)+Var(X1)-2Cov(X1*X2) cov(x1x2)=corr(x1x1)*sqrt(varx1)*sqrt(varx2)=0.3*sqrt(2)*sqrt(8)=1.2 var(y)=2+8-2*1.2=7.6

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