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 475 and a standard deviation of 16 (in millions of dollars). In addition, he believes that imports will have a mean of 85 and a standard deviation of 15 (in millions of dollars). Finally, he believes that the correlation between imports and exports will be -0.24. 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: 390.00 Standard deviation: Enter an inte or decimal number, accurate to 2 decimal placesmore

Explanation / Answer

Solution:

Here we need to find the mean and standard deviation of trade balance. Mean is already given.

Mean = 390.00

Variance of trade balance =V(Z) = V(X) + V(Y) + 2*r*(V(X)*VY)) =162 + 152 + 2*(-0.24)*16*15

                                                                                            =162 + 152 + 2*(-0.24)*16*15
                                                                                            = 256 + 225 -115.2

                                                                                             = 481 - 115.2 = 365.8

Hence std deviation of trade balance =(365.8)1/2 =19.12

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