Probability Equations/Terms

empirical probability

comes from the long-run relative frequency of the event’s occurrence

theoretical probability

comes from a model

personal probability

subjective and represents personal degree of belief

law of large numbers

as the number of trials increases, the probability gets closer to a single number

law of averages

untrue belief that if an outcome hasn’t occurred for a while, it should occur soon

addition rule (must be disjoint)

P(A ∪ B)

multiplication rule (must be independent)

P(A ∩ B)

multiplication rule

P(A) × P(B|A)

addition rule

P(A) + P(B) - P(A ∩ B)

independence

P(B|A) = P(B)

mean

μ

variance

σ²

standard deviation

σ

E(X ± c)

E(X) ± c

var(X ± c)

var(X)

SD(X ± c)

SD(X)

E(aX)

a × E(X)

var(aX)

a² × var(X)

SD(aX)

√var(aX)

E(X ± Y)

E(X) ± E(Y)

var(X ± Y)

var(X) + var(Y)

SD(X ± Y)

√var(X + Y)