Problem 6. Suppose (X₁, X₂) have joint density (1₁,1₂)= [6x₁1² 0

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Problem 6. Suppose (X₁, X₂) have joint density
[6x₁x² 0<x₁ <1,0 < £2 <1
otherwise.
(₁,₂)=
a) Find the joint density of (Y₁, Y₂) where Y₁ = X² and Y₂ = X1 X2.
b) Find the density of Z = X₁X² by first finding the joint density of Z and U = X2, then
computing the marginal density of Z.
Transcribed Image Text:Problem 6. Suppose (X₁, X₂) have joint density [6x₁x² 0<x₁ <1,0 < £2 <1 otherwise. (₁,₂)= a) Find the joint density of (Y₁, Y₂) where Y₁ = X² and Y₂ = X1 X2. b) Find the density of Z = X₁X² by first finding the joint density of Z and U = X2, then computing the marginal density of Z.
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