19.X. Poisson Distribution – Detailed Study

Try these first

1. 1.

   What are the parameters of a Poisson distribution?

   Hint

   Remember it represents the average number of events.

2. 2.

   List one application of the Poisson distribution.

   Hint

   Think about where you would see random events.

3. 3.

   What is the probability mass function of a Poisson distribution?

   Hint

   Remember the structure of the PMF.

4. 4.

   Is the mean of a Poisson distribution equal to its variance?

   • True
   • False

   Hint

   Think of the properties we discussed.

5. 5.

   A bookstore sells an average of 4 novels per week. What is the probability that during a week, exactly 6 novels will be sold?

   Hint

   Identify λ and k first.

6. 6.

   Two independent machines produce widgets with a defect rate modeled by Poisson distributions of λ1 = 3 and λ2 = 2. What is the probability of a total of 4 defects?

   Hint

   You’ll need to sum the means before calculating.