Question

Every working day the number of students visiting library follows a non homo- geneous Poisson process with rates: 50 per hour from 8 : 00am to 10 : 00am, 100 per hour between 10 : 00am and 2 : 00pm, 80 per hour between 2 : 00pm and 5 : 00pm and 40 per hour between 5 : 00pm and 8 : 00pm. The average number of products that each student buys is 3.

(1) What is the distribution of the number of customers who visit library every working day (from 8 : 00am until 8 : 00pm) ?

(2) What is the expected number of products that library sells every working day?

Answer 1

1.

no. of customer :

average rate = sum of (rate*hours) / total hours

= ( 50*2 + 100*4 + 80*3 + 40*3 ) / (2+4+3+3)

= 71.67

distribution :

P(k customers) = e^(-71.667*12) * (71.667*12)^k / (k!)

2.

E(no. of products) = sum of time * rate * avg products per student

= 50*2*3 + 100*4*3 + 80*3*3 + 40*3*3

E(no. of products) = 2580

P.S. (please upvote if you find the answer satisfactory)