Key Terms
Random Variable
Describes the outcomes of a statistical experiment in words. Values change with each repetition of the experiment.
Example
X = number of heads when tossing three coins. x = 0, 1, 2, or 3.
Discrete Random Variable
Takes on countable values. You can list every possible outcome.
Discrete Probability Distribution Function (PDF)
Two rules, no exceptions. 1.
Formula
Sigma = square root of [ sum of (x - mu)^2 * P(x) ]
Law of Large Numbers
As the number of trials increases, the relative frequency of outcomes approaches the theoretical probability. The gap cl
EXAMPLE
Lottery game. Match all five numbers (0-9, with replacement) to win $100,000.
How to calculate
1. Use the same table; add a fourth column: (x - mu)^2
NOT BINOMIAL EXAMPLE
Drawing names from a hat without replacement. The probability changes after each draw, so trials are not independent.
Read
X is a random variable with a Poisson distribution, mean mu.
Mean
Mu (given or scaled from rate) Std Dev: sigma = square root of mu Variance: sigma^2 = mu x = 0, 1, 2, 3, ... Binomi
Deviation
Sigma = square root of (npq)
BERNOULLI TRIAL
A single trial with exactly two outcomes. Any binomial experiment is just a series of Bernoulli trials (n = 1 per trial)
Key difference from binomial
Binomial counts successes in a fixed number of trials; geometric counts trials until the first success (no fixed n).
X takes values
1, 2, 3, 4, ... (starts at 1; you always have at least one trial)