The number of failures of a car per year follows a Poisson d

The number of failures of a car per year follows a Poisson distribution with an average of 4 failures per year.

a. What is the probability that the car will fail 2 times in a year?

b. What is the probability that the car will fail 6 times in 5 years?

c. If you will sell the car as soon as it fails 3 times, what is the probability that you will keep the car for at least 2 years?

The number of failures of a car per year follows a Poisson distribution with an average of 4 failures per yea 3- a. b. c. What is the probability that the car will fail 2 times in a year? What is the probability that the car will fail 6 times in 5 years? If you will sell the car as soon as it fails 3 times, what is the probability that you will keep the car for at least 2 years?

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
a)
P( X = 2 ) = e ^-4 * 4^2 / 2! = 0.1465

b)
Mean rate of failure per year is 4
For 5 years it is = 4*5 = 20
P( X = 6 ) = e ^-20 * 20^6 / 6! = 0.0002

c)
Mean rate of failure for 2 year period is = 4*2 = 8
We sold the car atlest it gets 3 failure.
In 2 years if e get below 2 defects, i.e we kept the car for atleast 2 years.
P( X < = 2) = P(X=2) + P(X=1) + P(X=0)   
= e^-8 * 8 ^ 2 / 2! + e^-8 * 4 ^ 1 / 1! + e^-8 * ^ 0 / 0!
= 0.0138