A quality control unit in ball-bearing manufacturing company keeps record of error in terms of the number of faulty balls (W) per a lot. The size of standard lot is 8, and the probability distribution of single lot containing faulty balls is known as follows: W 1 2 3 4 5 6 7 8 Probability(W=w) 0.6 0.2 0.07 0.06 0.03 0.02 0.01 0.01 a. Construct a table for the cumulative probability distribution of W. b. Determine the expected number of faulty balls per lot, i.e. E[W], and the variance, V[W]. c. Construct a table for the probability distribution of W2 . d. Based off of b) and c), show that V [W]=E[W2 ]-E[W] 2 e. Find P (W?5).