Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is .4 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. a. ?Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] b.? ?Obtain the cumulative distribution function of X, and use it to calculate P(2? X ? 6).

Problem 20E Answer: Step1: We have Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is .4 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. We need to find, a. Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] b. Obtain the cumulative distribution function of X, and use it to calculate P(2 X 6). Step2: Let X be the number of people who arrive late for the seminar. Probability that late arrival of a couple or an individual is 0.4. Probability of arrival on time is 1 - 0.4 = 0.6 We have Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Each individual as two outcomes either comes on late or time. 5 Therefore the total possible outcomes are 2 = 32. a). 1).Consider, X = 0 (when no one is late) P(X = 0) = P(#1)×P(#2)×P(#3)×P(#4)×P(#5) = 0.6×0.6×0.6×0.6×0.6 = 0.07776. 2).Consider, X = 1 (one individual late) So we need to find probability of one P(X = 1) = {[ P(#1)×P(#2)×P(#3)×P(#4)× P(#5)] + [P(#1)×P(#2)×P(#3)× P(#4) ×P(#5)]} = {[0.6×0.6×.06×0.6×0.4] + [0.6×0.6×0.6×.04×0.6]} = {0.05184 + 0.05184} = 0.10368 3).Consider,X = 2 (one couple is late or both individual are late) So we do for one couple and multiply by 3 P(X = 2) = {[P(#1) ×P(#2)×P(#3)×P(#4)× P(#5)]+[P(#1) × P(#2) ×P(#3)×P(#4)× P(#5)]+[P(#1) ×P(#2)× P(#3) ×P(#4)× P(#5)]+[P(#1) ×P(#2)× P(#3) × P(#4) × P(#5)]} = {[0.4×0.6×0.6×0.6×0.6] +[0.4×0.6×0.6×0.6×0.6]+[0.4×0.6×0.6×0.6× 0.6]+ [0.6×0.6×0.6×0.4×0.4]}...