Consider a Poisson distribution with a mean of two occurrenc

Consider a Poisson distribution with a mean of two occurrences per time period.

a.Compute the probability of three occurrences in two time periods (to 4 decimals).

b.Compute the probability of four occurrences in three time periods (to 4 decimals).

c.Compute the probability of six occurrences in one time period (to 4 decimals).

Solution

Here X is the number of occurrences with mean of 2 occurrences per time period.

a)

Required Probability, P(X=3) where X~poisson(mean=4)

P(X=3)=e^(-4) *4³ /3! =(32/3)*e^-4 =0.1954

b)

Required Probability,

P(X=4) where X~Poisson(mean=6)

P(X=4)=e^(-6) *6⁴ /4!=54*e^(-6) =0.1338

c)

Required Probability, P(X=6) where X~poisson(mean=2)

P(X=6)=e(-2)*2⁶ /6! =4/45*e^(-6) =0.0002