Exercise 1:

Computer chips allen contain defects. For a certain type of computer chip, the probability moss function of the number of defects X is given by (where c 2 0 is a conskulk: (x) = ox * for x = 0. 1. 2.3.4 and O ocheraise. (al What is the value of c? (hi Find the variance of X. (c) Suppose 1 0 computer chips are randomly selected. What is the probability that at least 3 of the computer chips have 2 defects?A system has six components connected as shown in the following diagram: A Assume A, B. C, D. E. and F function independently. If the probabilities that A, B. C. D. E. and F fail are 0.01, 0205. 0.02, 0.08. 0.10, and 0.05 respectively, what is the probability that the system fails