Question

PROBLEM 18.1 (pg 132, #86) People randomly arrive for treatment at an emergency room at a rate of 3.8 per hour. Let Y be the amount of time (in hours) until the next patient arrives in the emergency room. a. The random variable Y has an exponential distribution with parameter λ b. Find the probability no patients arrive over the next 2 hours or P(Y> 2). c. Find the median of Y d. What is the expected elapsed time until the next patient arrives or E[M? e. Find Var[Y]. PROBLEM 18.2 (pg 170, #63) Suppose that the duration of a phone call (in minutes) for a certain person can be modeled as an exponential distribution with parameter A. This person is trying to decide between two calling plans. Let X = the call duration. The first plan charges $0.10 per call plus $0.05 a minute and thus, on average, a phone call will cost E[0.10+ 0.05X]. The second plan charges S0.40 per call plus $0.02 per minute and thus, on average, a phone call will cost E[0.40+0.02X]. What is the expected cost of a phone call under the first plan? Note that the answer will be an expression containing A. a. b. What is the expected cost of a phone call under the second plan? c. A is a parameter which can be any positive number. For which values of A is the first plan more cost efficient than the second plan. Note: the expected call duration is E[X] 1/A

Answer 1