Question

(Poisson Distribution) The number of students that come to Professor Johnson’s office hours each day is a Poisson distribution with mean 3.

(a) What is the probability that exactly 3 students come to office hours today?

(b) What is the probability that two or fewer students come to office hours today?

(c) What is the probability that more than two students come to office hours today?

(d) What is the variance of the number of students that come to office hours each day?

Answer 1

(a)

Probability Mass Function of X with mean = = 3 is given by:

                   for x 0, 1,2,...

For x = 3:

(b)

P(X2)= P(x=0) + P(x=1) + P(x=2)

So,

P(X2) = 0.4232

So,

Answer is:

0.4232

(c)

P(X>2) = 1- [P(X=0)+P(X=1)+P(x=2)]

So,

P(X>2) = 1 - 0.4232 = 0.5768

So,

Answer is:

0.5768

(d)

Variance of number of students = Variance of Poisson Distribution = = 3

So,

Answer is:

3