Question

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

1. Which of the following is the appropriate Poisson probability function for one time period?
   

   1
   2
   3

   
   
   SelectEquation #1Equation #2Equation #3
   
2. What is the expected number of occurrences in three time periods?
   
   
3. Select the appropriate Poisson probability function to determine the probability of x occurrences in three time periods.
   

   1
   2
   3

   
   
   SelectEquation #1Equation #2Equation #3
   
4. Compute the probability of two occurrences in one time period (to 4 decimals).
   
   
5. Compute the probability of four occurrences in three time periods (to 4 decimals).
   
   
6. Compute the probability of seven occurrences in two time periods (to 4 decimals).

Answer 1

a)

lambda = mean = 2

b)

for 3 periods

expected number = 2 * 3 = 6

c)

for 3 time period

mean = 6

hence

d)

P(X = 2) = e^(-2) *2^2/2! = 0.2707

e)

P(Y = 4) = e^(-6) * 6^4/4! = 0.1339

f)

P(Z = 7) = e^(-4) *4^7/7! = 0.0595

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