10. Suppose that X, Y and Z are normally distributed where X ?N(100,100), Y ? N(400, 400) and
Z ? N(64,64). Let W = X + Y + Z.
a) Describe the distribution of W, give a name and parametersE(W) and Var(W).
b) Use Excel or R to generate 200 random values for X, Y and Z.Add these to obtain 200 values for W. Create a histogram for W. InExcel use the NORMINV(rand(),mean, sd) function.
c) Estimate E(W) and Var(W) using the random numbers.
