Chapter 4: Some Discrete Distributions

1. State three random variable models that can be constructed using independent Bernoulli trials.
2. State the probability mass function of a geometric random variable \(N\) with parameter \(p\), and state its mean and variance.
3. Give a constructive definition of a geometric random variable in terms of Bernoulli random variables.
4. Translate to and from the “number of trials needed for 1st success” geometric model and the “number of failures needed for 1st success” geometric model.
5. State the probability mass function of a negative binomial random variable \(N\) with parameters \((r, p)\), and state its mean and variance.
6. Give a constructive definition of a negative binomial random variable in terms of Bernoulli random variables.
7. Give a constructive definition of a negative binomial random variable in terms of geometric random variables.
8. Translate to and from the “number of trials needed for \(r\)-th success” negative binomial model and the “number of failures for \(r\)-th success” negative binomial model.