The chi-square distribution χ²(k) with k degrees of freedom is the distribution of Σ_i^k Z_i² where Z_i ~ iid N(0,1). Probability density: f(x|k) = x^(k/2-1)·exp(-x/2)/(2^(k/2)·Γ(k/2)), support x ∈ (0,∞). Moments: E[χ²] = k (mean equals…
The chi-square distribution χ²(k) with k degrees of freedom is the distribution of Σ_i^k Z_i² where Z_i ~ iid N(0,1). Probability density: f(x|k) = x^(k/2-1)·exp(-x/2)/(2^(k/2)·Γ(k/2)), support x ∈ (0,∞). Moments: E[χ²] = k (mean equals…