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-μμx/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
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.
1 answer