19.X.2.1. Mean and Variance

Try these first

1. 1.

   What is the mean and variance of a Poisson distribution?

   Hint

   Think about the properties of the Poisson distribution.

2. 2.

   Define the term λ in the context of the Poisson distribution.

   Hint

   It is the same for mean and variance.

3. 3.

   What is the mean of a Poisson distribution?

   • λ
   • λ²
   • 2λ

   Hint

   Recall the basic properties of the distribution.

4. 4.

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

   • True
   • False

   Hint

   Consider which values are equal in this context.

5. 5.

   A wildlife researcher measures an average of 3 bear sightings per day in a forest. What are the mean and variance of this daily event? How could this information aid in understanding bear behavior?

   Hint

   Consider how consistent averages can impact planning and management.

6. 6.

   In a manufacturing context, if a factory produces an average of 8 defects per job, and you need to analyze what the variance would tell you for quality control, how would you approach this?

   Hint

   Explore the implications of variability in product quality management.