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 455 and a standard deviation of 16 (in millions of dollars). In addition, he believes that imports will have a mean of 75 and a standard deviation of 27 (in millions of dollars). Finally, he believes that the correlation between imports and exports will be -0.25. 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: 75 Standard deviation:

Explanation / Answer

Mean of trade balance = mean of exports - mean of imports

= 455 - 75

= 380

Cov(imports and exports) = cor(imports and exports) * standard of (imports) * standard deviation (exports)

= (-0.25)*27 * 16

= - 1728

Variance of trade balance = Variance of exports + Variance of imports - 2*cov(exports and imports)

= 162 + 272 + 2 * 1728

= 4441

Standard deviation of trade balance = sqrt(4441)= 66.64

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