SOCR EduMaterials FunctorActivities Bernoulli Distributions

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.\( X \sim Bernoulli(0.5) \)
  • b.\( X \sim Binomial(1,0.5) \)
  • c.\( X \sim Geometric(0.5) \)
  • d.\( X \sim NegativeBinomial(1, 0.5) \)

Below you can see a snapshot of the MGF of the distribution of \( X \sim Bernoulli(0.8) \)

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