Question

A small firm has 22 desktop computers in the office. The computers are not networked, so they behave independently of each other. The probability that an individual computer breaks down in a calendar year is 0.1.

(a) What is the distribution of the number of computers that break down in a year? Write down the pmf.

(b) What is the probability that no computers break down in a year?

(c) What is the probability that two or more computers break down in a year?

(d) What is the expected number of computers that break down in a year?

(e) What is the variance of the number of computers that break down in a year?

Answer 1

Let X be the no. of computers that break down in an year.
X~Binomial(22,0.1)

a)PMF is given as:

b)probability of no break down in a year:

c)Probability of 2 or more break down in an year:

d) Since X follows binomial distribution the expected no. of breakdown in an year is given as:

E(X)=n*p where n=22 and p=0.1
E(X)=2.2 breakdowns in a year

e)

Variance is given as :n*p*(1-p)=22*0.1*0.9=1.98 breakdowns