Question

Determine each of the following distributions (Bernoulli, Binomial, Geometric and Poisson)

The average number of homes sold by the Acme Realty company is 2 homes per day. What is the probability that exactly 3 homes will be sold tomorrow?

Answer 1

Solution:

Given: The average number of homes sold by the Acme Realty company is 2 homes per day.

A random variable x is said to follow a Poisson distribution, if there are number of occurrences over some time period or space with average .

Thus given random variable x = number of homes sold by the Acme Realty company per day can have values 0,1,2,3,... so on.

Thus x =  number of homes sold by the Acme Realty company per day follows Poisson distribution with parameter homes per day.

What is the probability that exactly 3 homes will be sold tomorrow?

P( X= 3) =.........?

Probability mass function of Poisson distribution is: