19.X.3. Derivation of Poisson Distribution as a Limit of Binomial Distribution

Try these first

1. 1.

   In a Binomial distribution, what parameters define the model?

   Hint

   Think about what characterizes a Binomial experiment.

2. 2.

   What does the λ (lambda) represent in the Poisson distribution?

   Hint

   This is a rate parameter.

3. 3.

   What is the condition necessary for the Binomial distribution to approach the Poisson distribution?

   • n becomes finite
   • n approaches infinity and p approaches zero
   • p becomes 1

   Hint

   Consider 'infinity' as a keyword.

4. 4.

   True or False: The mean and variance of the Poisson distribution are both equal to λ.

   • True
   • False

   Hint

   Recall the properties of the Poisson distribution.

5. 5.

   A renewable energy facility produces, on average, 20 power outages per month. Calculate the probability of having exactly 5 outages next month. Use λ=20.

   Hint

   Convert the values into the Poisson formula carefully.

6. 6.

   Discuss how you would use the Poisson distribution to model the call volume in a call center with an average of 10 calls per hour. What assumptions must be kept in mind?

   Hint

   Think about independence and rate stability.