19.X.2. Properties of Poisson Distribution

Try these first

1. 1.

   What is the mean of a Poisson distribution represented by λ?

   Hint

   Remember, λ stands for the average number.

2. 2.

   True or False: The variance of a Poisson distribution is different from its mean.

   Hint

   Check if both values are defined by the same parameter.

3. 3.

   What is the mean of a Poisson distribution?

   • λ
   • λ^2
   • 2λ

   Hint

   Think back to how we defined λ earlier.

4. 4.

   True or False: The sum of two independent Poisson variables is also Poisson.

   • True
   • False

   Hint

   Recall the additive property discussed.

5. 5.

   A bookstore receives an average of 10 customers per hour. Calculate the probability that exactly 15 customers will visit in the next hour.

   Hint

   Rewrite the PMF equation and plug in the values for λ and k.

6. 6.

   In a factory, defective items occur with a mean rate of 0.5 defect per meter. Find the probability of having no defects in a 5-meter stretch of items.

   Hint

   Identify the λ first, then apply the Poisson PMF for k = 0.