# Consider a Poisson distribution with a mean of three occurrences per time period. (a) Write the appropriate Poisson probability function f(x)

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Question:

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

(a) Write the appropriate Poisson probability function f(x)

(b) What is the expected number of occurrences in four time periods?

(c) Write the appropriate Poisson probability function to determine the probability of x occurrences in four time periods f(x)

(d) Compute the probability of three occurrences in one time period. (Round your answer to four decimal places.)

(e) Compute the probability of twelve occurrences in four time periods. (Round your answer to four decimal places.)

(f) Compute the probability of nine occurrences in three time periods. (Round your answer to four decimal places.)

We are given that: a Poisson distribution with a mean of three occurrences per time period.

Part a) We have to write the appropriate Poisson probability function.

A Poisson probability function with parameter $\lambda$ is given by:

$f(x)= \frac{e^{-\lambda} \times \lambda^{x}}{x!}$

For Poisson distribution , parameter $\lambda$ is the mean.

Thus $\lambda$ = 3 ,