25 Suppose that X₁ and X₂ have a joint pdf f(x₁, x₂) = (2/3)(x₁ + 1), for 0 < x₁ < 1,0 < x₂ < 1,
25 Suppose that X₁ and X₂ have a joint pdf f(x₁, x₂) = (2/3)(x₁ + 1), for 0 < x₁ < 1,0 < x₂ < 1,
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 6E
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Question
solve second vi, vii, viii please
Thank you
![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)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf4d5614-e5fa-4399-aabc-c345eeef0588%2F437f1abf-f311-4b00-b566-f57cb7794d70%2Flfsfhf_processed.png&w=3840&q=75)
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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