Probability and Statistics
Probability and Statistics tests probability rules, distributions and statistical inference. Expect conditional probability, independence, binomial and Poisson models, normal approximation, sampling and hypothesis tests.
Core rules
- P(A|B)=P(A∩B)/P(B). A and B are independent iff P(A∩B)=P(A)P(B). Mutually exclusive means P(A∩B)=0.
- Binomial B(n,p): mean np, variance np(1-p). Poisson Po(λ): mean=variance=λ, used for counts.
- Normal: standardise z=(x-μ)/σ; use continuity correction when approximating discrete counts.
- Hypothesis test: state H0 and H1, compute the test statistic or p-value, compare with the significance level, and conclude in context.
Worked example
Machine A makes 60% of items with 2% defective; machine B makes 40% with 5% defective. P(defective)=0.6(0.02)+0.4(0.05)=0.032. Given defective, P(A)=0.012/0.032=0.375. The denominator is total defective probability, not P(A).
Traps
Confusing independent with mutually exclusive; forgetting continuity correction; using sample variance as population variance; saying you accept H0 instead of failing to reject it; ignoring the context in the final conclusion.