Buses arrive at a city according to a Poisson process with a rate of 5 per hour. (a) What is the probability that no buses arrive between 9 a.m. and 11 a.m. on a randomly selected morning? (b) Given...

Buses arrive at a city according to a Poisson process with a rate of 5 per hour. (a) What is the probability that no buses arrive between 9 a.m. and 11 a.m. on a randomly selected morning? (b) Given three buses have arrived in the first hour, what is the probability that the next bus arrives in the next 1/2 an hour? (c) What is the probability that the fifth bus of the day arrives after midday given they start arriving at 9 a.m. (d) What is the probability that at most 2 buses arrive in the first hour?
The management at a fast-food outlet is interested in the joint behaviour of the random variables X and Y. X is the total time a customer waits between arriving at the store and receiving their food. Y is the time the customer waits in the line. The joint distribution is
f (x , y)
0(a) Find fi(x), the marginal distribution of X. (b) Find E[X], the expected value of X. (c) Find f (y1x), the conditional distribution of Y given X = x. (d) Are X and Y independent?


1. 2. 3. 4. 5. 6. 7. 8. 9.