Key points
- Independent events: P(A ∩ B) = P(A) · P(B).
- Mutually exclusive: P(A ∪ B) = P(A) + P(B).
- E[X + Y] = E[X] + E[Y] always; Var(X + Y) = Var(X) + Var(Y) only if independent.
- Var(X) = E[X²] − (E[X])².
Notes / GATE / Probability and Statistics
CH 01Probability essentials
Probability and Statistics · GATE
Formulas & facts
- Bayes
- P(A|B) = P(B|A)P(A) / P(B)
- Binomial mean / var
- np / np(1 − p)
- Poisson mean = var
- λ
- Exponential mean
- 1 / λ
- Uniform(a, b) mean / var
- (a + b)/2 / (b − a)²/12