5. Let the random variable X have a discrete uniform distribution on the integers 0 3 x3 99. Determine the mean and variance of X. 6. Thickness measurements of a coating process are made to the nearest hundredth of a millimeter. The thickness measurements are uniformly distributed with values 0.15, 0.16, 0.17, 0.18, and 0.19. Determine the mean and variance of the coating thickness for this process. 7. The random variable X has a binomial distribution with n = 10 and p = 0.5. Determine the following probabilities: 7.1 P(X = 5) 7.2 P(XS2) 73 P(X > 7) 7.2 Determine the mean and variance of X. 8. The phone lines to an airline reservation system are occupied 40% of the time. Assume that the events that the lines are occupied on successive calls are independent. Assume that 10 calls are placed to the airline. 8.1 What is the probability that for exactly three calls, the lines are occupied? 8.2 What is the probability that for at least one call, the lines are not occupied? 8.3 What is the expected number of calls in which the lines are all occupied? 9. A multiple-choice test contains 25 questions, each with four answers. Assume that a student just guesses on each question. 9.1 What is the probability that the student answers more than 20 questions correctly? 9.2 What is the probability that the student answers fewer than 5 questions correctly? 10. The probability that a wafer contains a large particle of contamination is 0.01. If it is assumed that the wafers are independent, what is the probability that exactly 125 wafers need to be analyzed before a large particle is detected? 11. Suppose that the random variable X has a geometric distribution with p = 0 5. 11.1 Determine the following probabilities: P(X =4), P(X =3), P(X > 3) 11.2 Determine the mean and variance of X