Section 3.5: The Binomial Probability Distribution

1. Identify the 4 characteristics of a binomial experiment, and determine whether a given experiment has those characteristics.
2. Determine the sample space for a given binomial experiment.
3. State in what way a binomial random variable acts as a function from the sample space of a binomial experiment. That is, what does the binomial random variable output for a given outcome in the sample space?
4. State the probability mass function for a binomial random variable with parameters \(n\) and \(p\).
5. Identify the parameters of a binomial random variable for a given binomial experiment.
6. Use the formula for the probability mass function of a binomial random variable to compute \(P(X = x; n, p)\) directly.
7. Use the probability mass function or cumulative distribution function for binomial random variables to compute \(P(X = x; n, p), P(X \leq x; n, p), P(X > x; n, p),\) etc., using R
   • i.e. For any probability query \(P(X \in Q)\), use dbinom or pbinom to answer the query.
8. State the mean and variance of a binomial random variable, and compute the mean and variance from a given binomial experiment.