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
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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Could you solve parts m, n, and o please?
Thank you
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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