Revision sheet

Discrete distributions

• Values with probabilities in $[0, 1]$ summing to 1.
• Add probabilities for events.

Watch out: values are not automatically equally likely.

Expected value and SD

$E(X) = \sum x P(x)$; $\text{SD} = \sqrt{\sum (x - \mu)^2 P(x)}$.

Watch out: weight by probabilities; include losses.

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.