Question

I need help on the steps and logic used to get the solution provided.

Assume that the copy machine breaks down at any time and that the breakdowns occur as a time-homogeneous Poisson process with an average of 2 breakdowns per week.

a) In a one week period, what are the mean and SD number of breakdowns? (Answer 2, root 2)

b) In a two week period, what are the mean and SD number of breakdowns? (Answer 4, 2)

c) What is the probability there are exactly 3 breakdowns in the next week? (Answer 0.1804)

d) What is the probability there are exactly 4 breakdowns in the next two week period? (Answer 0.1954)

e) What is the probability there are more than 7 breakdowns in a three week period? (Answer 0.2560)

f) What is the probability that in a 3 week period the number of breakdowns is within one SD of the mean? (Answer 0.696)

Answer 1

Ans:

Given that

mean rate,=2 per week

For Poisson distribution,

mean=

standard deviation=sqrt()

a)For one week,mean rate =2*1=2

mean=2

standard deviation=sqrt(2)

b)For two week,mean rate=2*2=4

mean=2*2=4

standard deviation=sqrt(2*2)=2

c)

P(x=3)=e^-2*(2^3/3!)=0.1804

d)

P(x'=4)=e^-4*(4^4/4!)=0.1954

e)For 3 weeks,mean rate =2*3=6

P(x>7)=1-P(x<=7)=1-Poisson(7,6,true)=0.2560