Revision sheet

Basics

• Equally likely: favorable ÷ total.
• $P(\text{not } A) = 1 - P(A)$; "at least one" via the complement.

Watch out: make sure the outcomes really are equally likely.

Long run

• Probability = long-run relative frequency.
• Simulate with random numbers.

Watch out: no memory, no "due" outcomes.

Trees

• Multiply along paths; add paths to the same end.
• $P(A \mid B) = P(A \text{ and } B)/P(B)$.

Watch out: with rare events, most positives can be false.

Population and sample

• Population → parameter (usually unknown).
• Sample → statistic (an estimate).

Watch out: a number from the sample is a statistic.

Bias

Voluntary response, convenience, undercoverage, nonresponse, response bias.

Watch out: a bigger biased sample is still biased.

Sampling variability

• Statistics vary from sample to sample.
• Sampling distribution: a statistic over all samples.
• Larger $n$: less variability.

Watch out: data distribution vs sampling distribution.

Mean absolute deviation

Average distance from the mean.

Watch out: distances, not signed differences.

Spread

• Range, IQR (resistant), standard deviation.
• $s$ divides by $n - 1$; $s^2$ is the variance.

Watch out: the SD is the square root of the variance.