11. 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 the name and the distribution and parameters E(W) and Standard deviation(W).

b) Use R to generate 10,000 random values for X, Y and Z. Add these to obtain 10,000 values for W. Create histogram for W. Copy and Paste just the histogram into your homework paper.

c) Estimate E(W) and Standard Dev(W) using the random numbers.