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 0.32 (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.] (Round your answers to four decimal places.) Р(Х %3D х) 3 4 6. (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) 3 4 8. Use the cumulative distribution function of X to calculate P(2 < X < 6). (Round your answer to four decimal places.) P(2 < X < 6) =

00 Suppose that the probability that a particular computer chip fails after t= a hours of operation is 0.00002 - 0.00002t dt. e a a. Find the probability that the computer chip fails after 19,000 hr of operation (that is, the chip lasts at least 19,000 hr). b. Of the chips that are still in operation after 19,000 hr, what fraction of these will operate for at least another 19,000 hr? 00 c. Evaluate 0.00002 - 0.00002t dt and interpret its meaning. e a. The probability that the chip fails after 19,000 hr of operation is (Round to three decimal places as needed.) b. The fraction that will still be operating for at least another 19,000 hr is (Round to three decimal places as needed.) c. Choose the correct answer below. A. The probability that the chip fails immediately is 0.00002 - 0.00002t dt = B. The probability that the chip eventually fails is 0.00002 - 0.00002t dt = e C. The probability that the chip never fails is 0.00002 0.00002t dt = e D. There is not enough information to…

A fisherman catches fish according to a Poisson process with rate λ = 0.6 per hour. The fisherman will keep fishing for two hours. If he catches two or more fish after two hours, then he goes home. Otherwise, he continues until he catches a total of two fish (including those caught in the first two hours) and then goes home. (a) Find the probability that he stays for more than two hours. (b) Find the probability that he catches at least three fish. (c) Find the expected number of fish that he catches. (d) Find the expected total fishing time

A drawer holds purple socks and yellow socks. If n socks are taken out of the drawer at random, the probability that all are yellow is 1/2. What is the smallest possible number of socks in the drawer (as a function of n)?

a box contains 6 balls, 4 of which are red. I randomly select 3 balls from the box. Find the probability mass function of getting 2 red balls?