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Q1 Suppose X; ~ 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 independent and identically distributed, Z₂'s independent and identically distributed and X; 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!! (a) X₁ X₂ (d) Z² (e) (b) X₂ + 2X3 √n (x-μ) o Sz (c) X₁ - X₂ oSz√2 (f)_Z²+Z2

Q1 Suppose X; ~ 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 independent and identically distributed, Z₂'s independent and identically distributed and X; 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!! (a) X₁ X₂ (d) Z² (e) (b) X₂ + 2X3 √n (x-μ) o Sz (c) X₁ - X₂ oSz√2 (f)_Z²+Z2

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Could you solve parts d, e, and f please? 

Q1 Suppose X; ~ N(µ, o²), i = 1, 2,...,n and Z; ~ N(0, 1), i = 1, 2, ..., k, and all random variables are independent, i.e. X₂'s are independent and identically distributed, Z;'s independent and identically distributed and X; 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) (g) Z²-Z2 (j) Z₁ Z₂ Σ1(Χ; – μ)2 02 (b) X₂ + 2X3 √n (x-μ) o Sz (o) kŻ² (h) (P) Z₁ Z2 (²) k + Σ(Z₁ - Z)² (c) X₁ - X₂ oSz√2 (f) Z²+Z2 Z² Z2 (i) √nk (X-μ) k °√ CL1Z? X Σi=1²₁ 02 k (n) + (k − 1) Σ1 (X; – X)² (n − 1)0² Σh_1(Zi – Z)² k
Transcribed Image Text:Q1 Suppose X; ~ N(µ, o²), i = 1, 2,...,n and Z; ~ N(0, 1), i = 1, 2, ..., k, and all random variables are independent, i.e. X₂'s are independent and identically distributed, Z;'s independent and identically distributed and X; 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) (g) Z²-Z2 (j) Z₁ Z₂ Σ1(Χ; – μ)2 02 (b) X₂ + 2X3 √n (x-μ) o Sz (o) kŻ² (h) (P) Z₁ Z2 (²) k + Σ(Z₁ - Z)² (c) X₁ - X₂ oSz√2 (f) Z²+Z2 Z² Z2 (i) √nk (X-μ) k °√ CL1Z? X Σi=1²₁ 02 k (n) + (k − 1) Σ1 (X; – X)² (n − 1)0² Σh_1(Zi – Z)² k
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