Consider a maternity ward in a hospital. A delivery may result in one, two or three births with probabilities .9, .08, and .02, respectively independently from the previous ones. The number of deliveries forms a Poisson process with rate 10 per day.

i) Find the probability that no deliveries occur in an interval of 5 hours.

ii) Find the probability that at least one delivery occurs in a day.

iii) Find the mean and the variance of the number of births during a day.

iv) Using the built-in function poissrnd in MATLAB, program to simulate the number of births on in different days in the ward. Inputs: ,n(number of days)

Outputs:

a)a 1 n vector(array) with numbers generated in the program,

b) a histogram with the relative frequencies of the number generated

by the program.

c)a histogram with the cumulative frequencies of the number generated by the program.