Chapter 4: Some Discrete Distributions

1. Explain what it means for a random variable to have a parametric distribution.
2. State the probability mass function of a discrete uniform random variable \(X\) on \(\{a, a + 1, \ldots, b - 1, b\}\), and state its mean and variance in terms of both \((a, b)\) and \((a, n = b - a + 1)\).
3. Determine the mean and variance of a discrete uniform random variable with non-unit but constant spacing.
4. State what process a Bernoulli random variable models.
5. State the probability mass function of a Bernoulli random variable \(B\) with parameter \(p\), and state its mean and variance.
6. Give a constructive definition of a binomial random variable in terms of Bernoulli random variables.
7. State the probability mass function of a binomial random variable \(X\) with parameters \((n, p)\), and state its mean and variance.
8. State the four conditions that an outcome should satisfy to be well-modeled by a binomial random variable.
9. Compute binomial probabilities quickly using the TI–30XS’s Data functionality.