In the next year, an economist in a particular nation believes that exports will

Question

In the next year, an economist in a particular nation believes that exports will have a mean of 270 and a standard deviation of 27 (in millions of dollars). In addition, he believes that imports will have a mean of 75 and a standard deviation of 18 (in millions of dollars). Finally, he believes that the correlation between imports and exports will be -0.48. Define the trade balance as exports minus imports, Find the mean and the standard deviation of the trade balance (in millions of dollars ROUND YOUR ANSWERS TO TWO DECIMAL PLACES Mean: Standard deviation:

Explanation / Answer

as trade balance Z = export (X) -Import(Y)

hence mean of trade balance E(Z) =E(X)-E(Y) =270-75 =195

and std deviation SD(Z) =(Var(X)+Var(Y)-2*r*SD(X)*SD(Y))1/2 =(272+182-2*(-0.48)*27*18)1/2=38.98

please revert for any clarification required

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