Q5 Suppose that X₁ and X₂ have a joint pdf zero otherwise. f(x₁, x₂) = (2/3)(x₁ + 1), for 0 < x₁ < 1,0 < x₂ < 1, Q5 (i.) Find fx₁ (₁) Q5 (ii.) Find fx₂(x₂) Q5 (iii.) Find P(X₁ < 2X₂ < 3X₁) Q5 (iv.) Are X₁ and X₂ independent? Q5(v.) Find Var (X₂) Q5 (vi.) Find a pdf of X₂/X₁. Q5(vi.) Find P(1/2 < X₂/X₁ < 3/2) using the pdf of X₂/X₁. Q5 (vii.) Find the conditional pdf of X₂ given X₁ = ₁, fx₂|X₁ (x₂|x₁). Q5 (viii.) Find E(X2|X1). Q5 (ix.) Find Var(E(X₂|X1)). Q(x.) Find E(Var(X₂|X₁)).
Q5 Suppose that X₁ and X₂ have a joint pdf zero otherwise. f(x₁, x₂) = (2/3)(x₁ + 1), for 0 < x₁ < 1,0 < x₂ < 1, Q5 (i.) Find fx₁ (₁) Q5 (ii.) Find fx₂(x₂) Q5 (iii.) Find P(X₁ < 2X₂ < 3X₁) Q5 (iv.) Are X₁ and X₂ independent? Q5(v.) Find Var (X₂) Q5 (vi.) Find a pdf of X₂/X₁. Q5(vi.) Find P(1/2 < X₂/X₁ < 3/2) using the pdf of X₂/X₁. Q5 (vii.) Find the conditional pdf of X₂ given X₁ = ₁, fx₂|X₁ (x₂|x₁). Q5 (viii.) Find E(X2|X1). Q5 (ix.) Find Var(E(X₂|X1)). Q(x.) Find E(Var(X₂|X₁)).
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
Transcribed Image Text:Q5 Suppose that X₁ and X₂ have a joint pdf
zero otherwise.
f(x₁, x₂) = (2/3)(x₁ + 1), for 0 < x₁ < 1,0 < x₂ < 1,
Q5 (i.) Find fx₁ (₁)
Q5 (ii.) Find fx₂(x₂)
Q5 (iii.) Find P(X₁ < 2X₂ < 3X₁)
Q5 (iv.) Are X₁ and X₂ independent?
Q5(v.) Find Var (X₂)
Q5 (vi.) Find a pdf of X₂/X₁.
Q5(vi.) Find P(1/2 < X₂/X₁ < 3/2) using the pdf of X₂/X₁.
Q5 (vii.) Find the conditional pdf of X₂ given X₁ = ₁, fx₂|X₁ (x₂|x₁).
Q5 (viii.) Find E(X₂|X₁).
Q5 (ix.) Find Var(E(X₂|X1)).
Q(x.) Find E(Var (X₂|X₁)).
Transcribed Image Text:Q5 Suppose that X₁ and X₂ have a joint pdf
zero otherwise.
f(x₁, x₂) = (2/3)(x₁ + 1), for 0 < x₁ < 1,0 < x₂ < 1,
Q5 (i.) Find fx₁ (₁)
Q5 (ii.) Find fx₂(x₂)
Q5 (iii.) Find P(X₁ < 2X₂ < 3X₁)
Q5 (iv.) Are X₁ and X₂ independent?
Q5(v.) Find Var (X₂)
Q5 (vi.) Find a pdf of X₂/X₁.
Q5(vi.) Find P(1/2 < X₂/X₁ < 3/2) using the pdf of X₂/X₁.
Q5 (vii.) Find the conditional pdf of X₂ given X₁ = ₁, fx₂|X₁ (x₂|x₁).
Q5 (viii.) Find E(X₂|X₁).
Q5 (ix.) Find Var(E(X₂|X1)).
Q(x.) Find E(Var (X₂|X₁)).
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