Question

On an average a photocopier breaks down 1.3 times per week. Let X be the number of times it will break down next week. Assume that weather the copier breaks down again is independent of previous breakdowns, and that the number of breakdowns in a given length of time is proportional to the length of time. Find a)the probability of 2 breakdowns next week b) the expected number of breakdowns next week c) the variance and standard deviation of the number of breakdowns next week.

Answer 1

Here, X = Number of times a photocopier breaks down in a week

a)

Required probability =

b)

For Poisson distribution, Mean = E(X) = = 1.3

c)

For Poisson distribution, Variance = = 1.3

So, Standard deviation =