QUESTION THREE [40 Marks] i. Suppose that buses arrive are scheduled to arrive at a bus stop at noon but are always X minutes late, where X is an exponential random variable with probability density function FAX f(x)= he . Suppose that you arrive at the bus stop precisely at noon. a. Compute the probability that you have to wait for more than five minutes for the bus to arrive. b. Suppose that you have already waiting for 10 minutes. Compute the probability that you have to wait an additional five minutes or moreThe duration of time from first exposure to HIV infection to AIDS diagnosis is called the incubation period. The incubation periods of a random sample of 7 HIV infected individuals is given below (in years): 12.0 10.5 9.5 6.3 13.5 12.5 7.2 a. Calculate the sample mean. b. Calculate the sample median. c. Calculate the sample standard deviationd. If the number 6.3 above were changed to 1.5, what would happen to the sample mean, median, and standard deviation? State whether each would increase, decrease, or remain the same. e. Suppose instead of 7 individuals, we had 14 individuals. (we added 7 more randomly selected observations to the original 7) 12.0 10.5 5.2 9.5 6.3 13.1 13.5 12.5 10.7 7.2 14.9 6.5 8.1 7.9