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## Question 5 in the attach fileSTAT 67, Fall 2016Homework 411-10-2016 1. You are waiting for the bus t

Question 5 in the attach fileSTAT 67, Fall 2016Homework 411-10-2016 1. You are waiting for the bus to arrive to pick you up. You believe the wait time can be anynumber between 0 and 5 minutes, with uniform density.a. What is the probability that you wait less than 2.5 minutes?b. What is the expected time in minutes that you will be waiting for the bus? Interpret this incontext of the problem in a sentence or two.c. What is the probability that you wait between 1.5 and 3.5 minutes?d. Now say you wait for the bus 5 days in a row, with each day being independent of one another.What is the probability that you waited more than 2.5 minutes everyday?e. Continuing the scenario in part d., what is the probability that you waited more than 2.5 minutesat least one of the days?2. Cars arrive at an inspection station at a rate of 10 cars per hour. With probability of 0.5 a carwill pass inspection.a. What is the expected number of cars to arrive at the inspection station in 1 hour? What is theexpected number of cars to arrive in a 3 hour period?b. What is the probability that at most (less than or equal to) 15 cars will arrive in the 1 hour timeperiod? What is the probability that at most 45 cars will arrive in the 3 hour time period?c. In a 3 hour time period, what is the probability that more than 4 cars will arrive?d. Say the cars are independent of one another. What is the probability that 10 cars will arrive ina 1 hour time period AND all 10 will pass inspection. Hint: P(A and B)=P(A)*P(B|A)3. Let f (x) = cx3 and SX = [0, 2] (X is continuous).a. What value of c will make f (x) a valid density?b. What is P (X = 1)? What about P (X = 1 or X = 2)?i c. Find E(X).d. What is P (0.5