Q1 Suppose X₂ ~ N(μ, o²), i = 1, 2, ..., n and Z₂ ~ N(0, 1), i = 1, 2,... , k, and all random variables are independent, i.e. X, 's are ndependent and identically distributed, Zi's independent and identically distributed and X₁ and Z; are independent. State the distribution of each of the following random variables if it is named distribution or otherwise state 'unknown'. Justify your answers; no derivations are necessary!! (m) (a) X₁ - X₂ (d) Z2 (e) (9) 2² -Z2 (j) Z₁ Z2 Σ=1(X; – μ)2 02 (b) (o) kể X2 + 2X3 √n(X-μ) o Sz (p) (h) Z₁ Z2 k + Σ(Z₁ - Ž)² i=1 (k − 1) (n-1)0² (c) X₁ - X₂ oSz√2 (f) Z²+Z² Z² Z2 √nk (X-μ) vΣ 1Ζ (n) X 02 + ₁ (X; - X)² -1(Z; – Z)² ΣΖ, k

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