Question

Consider a Poisson distribution with a mean of two occurrences per time period.
a. Write the appropriate Poisson probability function.
b. What is the expected number of occurrences in three time periods?
c. Write the appropriate Poisson probability function to determine the probability of x
occurrences in three time periods.
d. Compute the probability of two occurrences in one time period.
e. Compute the probability of six occurrences in three time periods.
f. Compute the probability of five occurrences in two time periods.

Answer 1

Answer on Question #58142 – Math – Statistics and Probability

Question

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

a. Write the appropriate Poisson probability function.

b. What is the expected number of occurrences in three time periods?

c. Write the appropriate Poisson probability function to determine the probability of x occurrences in three time periods.

d. Compute the probability of two occurrences in one time period.

e. Compute the probability of six occurrences in three time periods.

f. Compute the probability of five occurrences in two time periods.

Solution

a. $P(x; \mu) = \frac{e^{-\mu} \mu^x}{x!} = \frac{e^{-2} 2^x}{x!}$

b. $N = \mu \times 3 = 6$

c. $P(x; 6) = \frac{e^{-6} 6^x}{x!}$

d. $P(2; 2) = \frac{e^{-2} 2^2}{2!} = 0.2707$

e. $P(6; 6) = \frac{e^{-6} 6^6}{6!} = 0.1606$

f. $P(5; 4) = \frac{e^{-4} 4^5}{5!} = 0.1563$

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