If a power failures occur according to a poisson distribution with an average of 3 failures every twenty weeks,calculate the probability that there will not be more than one failure during a particular week.

Question

If a power failures occur according to a poisson distribution with an average of 3 failures every twenty weeks,calculate the probability that there will not be more than one failure during a particular week.

Answer 1

where μ represents the frequency of occurrence (success) within a given time period (week).

In this case, failure is considered "success".

so

μ
=3 "successes" / 20 weeks
=3/20

By definition of the Poisson distribution,
P(x;μ)=e^-μμ^x/x!
where x∈Z
=P(0;μ)+P(1;μ)
=e^-(3/20)(3/20)⁰/0! +e^-(3/20)(3/20)¹/1!
=0.86+0.13
=0.99