Question

The daily number of arrivals of patients to an emergency room is a Poisson random variable with a mean of 144 patients per day. A day is 24 hours. (i) Let X be the time between two patients' arrival, what is the distribution of X? [1]. (ii) What is the density function of X? [1] (iii) It is 11:00 AM and a patient just arrived, what is the probability that the next patient will arrive by 11:10 AM? [2] (iv) What is the expected value of Y = 2X + 5? [1] (v) Use the normal approximation for the Poisson distribution to obtain the approximate probability that 156 or more people arrive in a day.

Name: a the daily number of arrivals of patients to an emergency room is a poisson random variable with a mean of 144 patients per daya day is 24 hours i let x be the time between two patients arr 41117
Uploaded: 2023-05-14T13:45:31-08:00
Duration: 1 min 37 s
Channel: Numerade
Description: a the daily number of arrivals of patients to an emergency room is a poisson random variable with a mean of 144 patients per daya day is 24 hours i let x be the time between two patients arr 41117

          The daily number of arrivals of patients to an emergency room is a Poisson random variable with a mean of 144 patients per day. A day is 24 hours.

(i) Let X be the time between two patients' arrival, what is the distribution of X? [1].
(ii) What is the density function of X? [1]
(iii) It is 11:00 AM and a patient just arrived, what is the probability that the next patient will arrive by 11:10 AM? [2]
(iv) What is the expected value of Y = 2X + 5? [1]
(v) Use the normal approximation for the Poisson distribution to obtain the approximate probability that 156 or more people arrive in a day.

Added by Kevin C.

Question

Please give Ace some feedback