(i.e. sample size 1), for parts (b) and (c) use the sample means to create the histograms. Copy and Paste just the histograms into your homework paper. Explain the differences in the histograms. You can do this using R if you prefer. 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 parameters E(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. In Excel use the NORMINV(rand(), mean, sd) function. c) Estimate E(W) and Var(W) using the random numbers. 11. Given the follow joint pmf p(x,y) N m X 1 0.25 0.25 0.00 2 0.10 0.25 0.15 a) Find the Cov(X, Y) and b) The correlation coefficient of X and Y lenovo