Q2 Cars arrive at a parking lot at a rate of 20 per hour. Assume that a Poisson process model is appropriate. Answer the following questions. No derivations are needed but a justification of your...

Could you do parts 8, 9, 10 please (last 3parts)

Extracted text: Q2 Cars arrive at a parking lot at a rate of 20 per hour. Assume that a Poisson process model is appropriate. Answer the following questions. No derivations are needed but a justification of your answers is necessary. Q2(i.) What assumptions are necessary to model the arrival of cars as a Poisson process? Q2(ii.) What is the expected number of cars that arrive between 10:30 a.m. and 12:45 p.m.? Q2 (iii.) Suppose you walk into the parking lot at 11:05 a.m.; how long do you have to wait on average to see a car entering the lot? Q2 (iv.) Assume that the lot opens at 8 a.m. what is the expected time at which the tenth car arrives at the parking lot. Q2(v.) What is the expected waiting time between the arrival of the 10th and 11th car? Q2(vi.) How is the waiting time between the arrival times of 10th and 12th car distributed? Write the density function of the waiting time. Q2(vii.) As an outsider, you watch the cars entering the parking lot for half an hour in the morning (between 9 a.m. and 10:30 a.m.) and then for half an hour during lunchtime (between 12 p.m. and 1:30 p.m.). What can you say about the number of cars arriving at the parking lot during the two half-hour periods? Q2(viii.) Suppose each car pays a flat fee of $5 when it enters. What is the expected amount of money the parking lot receives during an 8-hour day? Q2(ix.) Now assume that the amount of fee each car pays is a random variable, i.e. the fee is $3 or $5 or $6 with probabilities 1/4, 1/2, and 1/4 respectively. What is the expected amount of money the lot receives during an 8-hour day? Q2 (x.) {\it More realistic model:} Suppose the parking lot charges $5 for a whole 8-hour day, $2 for one hour and $3.5 for four hours so that it can attract a variety of customers. Assume that the cars pay the fees upon entering the lot (i.e. cars must choose one of the fees). Let us also suppose that 20% of the cars pay an 8-hour fee, 50% of the cars pay the 4-hour fee, and 30% pay a 1-hour fee. Calculate the expected amount of money the parking lot receives during an 8-hour day.