Statistical Methods Formula Cheat Sheet , Cheat Sheet of Mathematical Statistics

Download Statistical Methods Formula Cheat Sheet and more Cheat Sheet Mathematical Statistics in PDF only on Docsity! Statistical methods, Formula sheet for final exam Combinatorics • Number of ways to choose k out of n objects:( n k ) = n(n− 1) · · · (n− k + 1) k! = n! (n− k)!k! Basic probability Always true: • P (Ac) = 1− P (A) • P (A ∪B) = P (A) + P (B)− P (A ∩B) • P (A ∩B) = P (A)P (B|A) • P (Ac) = 1− P (A) • A, B mutually exclusive: P (A ∪B) = P (A) + P (B) • A, B independent: P (A ∩B) = P (A)P (B) • Conditional probability of A given B: P (A|B) = P (A ∩B) P (B) LTP and Bayes’ theorem P (A) = P (A|B)P (B) + P (A|Bc)P (Bc) P (B|A) = P (A|B)P (B) P (A|B)P (B) + P (A|Bc)P (Bc) Discrete random variables • Pmf: p(x) = P (X = x) Special distributions: • X ∼ bin(n, p): p(k) = ( n k ) pk(1− p)n−k, k = 0, 1, ..., n (# of successes) E[X] = np • X ∼ geom(p): p(k) = (1− p)k−1p, k = 1, 2, ... (wait for first success) E[X] = 1 p Continuous random variables • Pdf: f(x) = F ′(x), x ∈ R • Cdf: F (x) = ∫ x −∞ f(t)dt, x ∈ R Special distributions: • X ∼ unif [a, b]: f(x) = 1 b− a , a ≤ x ≤ b (choose “randomly”) E[X] = a + b 2 • X ∼ exp(λ): f(x) = λe−λx, x ≥ 0 (memoryless) E[X] = 1 λ • X ∼ N(0, 1): ϕ(x) = 1√ 2π e−x 2/2, x ∈ R • X ∼ N(µ, σ2) : Z = X − µ σ ∼ N(0, 1)