Question

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

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

Answer 1

a) The Poisson probability function is P(x; λ) = (e^-λ * λ^x) / x!. b) The expected number of occurrences in four time periods is 12 occurrences. c) The Poisson probability function to determine the probability of x occurrences in four time periods is P(x; λ = 3 * 4) = (e^-(3 * 4) * (3 * 4)^x) / x!. d) The probability of three occurrences in one time period is 0.0613 (rounded to four decimal places).

Step-by-step explanation:

a) The appropriate Poisson probability function is given by: P(x; λ) = (e-λ * λx) / x!

b) To find the expected number of occurrences in four time periods, we simply multiply the mean by the number of time periods: 3 * 4 = 12 occurrences.

c) The appropriate Poisson probability function to determine the probability of x occurrences in four time periods is: P(x; λ = 3 * 4) = (e-(3 * 4) * (3 * 4)x) / x!

d) To compute the probability of three occurrences in one time period, we use the Poisson probability function with λ = 3 and x = 3: P(3; 3) = (e-3 * 33) / 3! = 0.0613 (rounded to four decimal places).