SOCR EduMaterials FunctorActivities Bernoulli Distributions

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This is an activity to explore the Moment Generating Functions for the Bernoulli, Binomial, Geometric and Negative-Binomial Distributions.

• Description: You can access the applets for the above distributions at http://www.socr.ucla.edu/htmls/SOCR_DistributionFunctors.html .

• Exercise 1: Use SOCR to graph the MGF's and print the following distributions and answer the questions below. Also, comment on the shape of each one of these distributions:
  • a.
  • b.
  • c.
  • d.

Below you can see a snapshot of the MGF of the distribution of

Do you notice any similarities between the graphs of these MGF's between any of these distributions?

• Exercise 2: Use SOCR to graph and print the MGF of the distribution of a geometric random variable with p = 0.2,p = 0.7. What is the shape of this function? What happens when p is large? What happens when p is small?

• Exercise 3: You learned in class about the properties of MGF's If then