1. Computer chips often contain defects. For a certain type of computer chip, the probability mass function of the number of defects X is given by (where c > 0 is a constant): p(x) = cx1/2 for x = 0, 1, 2, 3, 4 and 0 otherwise. (a) What is the value of c? (b) Find the variance of X. (c) Suppose 10 computer chips are randomly selected. What is the probability that at least 3 of the computer chips have 2 defects?3. (8 points) A system has six components connected as shown in the following diagram: B F D C D C 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, 0.05, 0.02, 0.08, 0.10, and 0.05 respectively, what is the probability that the system fails