The Statistics component covers probability theory and statistical distributions — essential for interpreting data and making inferences in science, business, and economics.
P(A) = number of favourable outcomes / total outcomes. P(A\'s complement) = 1 - P(A). Addition rule: P(A or B) = P(A) + P(B) - P(A and B). Mutually exclusive: P(A and B) = 0. Independent: P(A and B) = P(A) × P(B). Conditional probability: P(A|B) = P(A and B)/P(B). Tree diagrams and Venn diagrams for visualisation. Permutations: nPr = n!/(n-r)! (order matters). Combinations: nCr = n!/(r!(n-r)!) (order doesn\'t matter).
X ~ B(n, p): n independent trials, each with probability p of success. P(X = r) = ⁿCᵣ pʳ (1-p)ⁿ⁻ʳ. Mean = np. Variance = np(1-p). Conditions: fixed number of trials, two outcomes (success/failure), constant probability, independent trials. Use cumulative binomial tables or calculator.
X ~ N(μ, σ²): continuous, bell-shaped, symmetric about mean. Standardise: Z = (X - μ)/σ, where Z ~ N(0, 1). Use standard normal tables for P(Z < z). 68-95-99.7 rule: 68% within 1σ, 95% within 2σ, 99.7% within 3σ. Inverse normal: given probability, find value. Hypothesis testing: test whether sample data provides evidence against a claimed parameter value. H₀ (null) vs H₁ (alternative). Significance level (usually 5%). Reject H₀ if test statistic falls in critical region.
Permutations count arrangements where order matters: selecting president, vice-president, and secretary from 10 people gives 10P3 = 720 (who gets which role matters). Combinations count selections where order does not matter: choosing 3 people from 10 for a committee gives 10C3 = 120 (just who is chosen, no specific roles). Formula: nPr = n!/(n-r)!, nCr = n!/(r!(n-r)!) = nPr/r!. Combinations are always less than or equal to permutations because we divide by r! to remove the ordering of selected items.
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