A photolithographic process etches contact windows through an oxide layer deposited on a silicon wafer used in integrated circuit fabrication. For each wafer the r. v. of interest is the number of windows that are not properly formed (unopened or too small or too large). Suppose that the distribution of this r. v. is as follows: No. defective window 0 1 2 3 4 5 Probability 0.5 0.2 0.1 0.1 0.05 0.05 1. Compute the mean u and standard deviation o of this distribution. 2. To estimate the average number of defective windows per wafer, a random sample of five wafers is inspected periodically. To find the distribution of the sample mean, simulate 500 samples of size five, compute their sample means and plot a histogram. Also, calculate the average and the standard deviation of the means. 3. comment on the shape of the empirical distribution of X. Does it look closely to the normal distribution? Repeat the simulation for a sample size of 10. Do you see any difference in the shape? 4. How close are the average of the sample means and their standard deviation calculated in (2) to their theoretical values ji and o/n, where u and o are calculated in (1) and n = 5?