Question: Given W = (aX + Y) 2 where X and Y are zero-mean random variables with variance 2 X = 4, and variance 2 Y

Given W = (aX + Y)² where X and Y are zero-mean random variables with variance ²_X = 4, and variance ²_Y = 16, respectively. Moreover, their correlation coefficient is r = - 0.5.

1. Find the expected value of W as function of a

2. Find the value of the parameter a that minimizes the mean value of W.

3. Find the minimum mean value

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