A. Random variables
1. definition
2. binomial random variable
3. binomial distribution
B. Binomial experiments
1. definition; four conditions
a. fixed number of trials
b. two mutually exclusive outcomes
c. trials are independent
d. probabilities remain constant for each trial
2. binomial distribution
theorem
3. Bernoulli trials
13.5 Essential Ideas
Binomial Experiment
A binomial experiment is an experiment that
meets four conditions.
(1) There must be a fixed number of trials; denote this
by n.
(2) There must be two possible mutually exclusive outcomes
for each trial. Call
them success
and failure.
(3) Each trial must be independent.
(4) The probability of success and failure must remain
constant for each trial.
Binomial Distribution Theorem
Let X be a random variable for the number
of success in n independent and identical repetitions
of an experiment with two possible outcomes, success
and failure. If p is the probability of success,
then for k = 0, 1, ... , n,
