Chi-Sq

Question 1

Mean & Variance

Answer 1

E(X) = k

Var(X) = 2k

Question 2

If r.v.’s X1, X2, …, Xk are normally & ind’t dist with
μi & σ²i, i = 1, 2, …, k, respectively, then,

Answer 2

∑((Xi - μi)/σi)² ~ X²_(k)

Question 3

If (X1, X2, …, Xn)’ is a r.s. ~ N(μ, σ²), then,

Answer 3

∑((Xi - μ)/σ)² ~ X²_(k)

Question 4

If X ~ N(μ, σ²), then (a) & (b)

Answer 4

((X-μ)²/σ)² ~ X²_(1)

X~N(0,1) then X² ~ X²_(1)