Random Variables and Binomial Distribution

Random variable X assigns numerical value to each outcome. Mean (expectation) E(X)=Σx⋅P(X=x). Variance V(X)=E(X²)-[E(X)]². Binomial distribution: n trials, each with success probability p. P(X=r) = ⁿCᵣ × pʳ × (1-p)^(n-r). Mean = np. Variance = npq where q=1-p. Used in: coin tosses, quality testing, genetics.