With reference to Example 3 22, verify that the three random variables X 1 , X 2 , and X 3 are not independent, but that the two random variables X 1 and X 3 and also the two random variables X 2 and X 3 are pairwise independent Example 3 22 Considering again the trivariate probability density of Example 3 19, Find the joint marginal density of X 1 and X 3 and the marginal density of X 1 alone f(x1,x2 x3) elsewhere

Question: With reference to Example 3.22, verify that the three random variables X 1 , X 2 , and X 3 are not independent, but that

With reference to Example 3.22, verify that the three random variables X₁, X₂, and X₃ are not independent, but that the two random variables X₁ and X₃ and also the two random variables X₂ and X₃ are pairwise independent.

Example 3.22

Considering again the trivariate probability density of Example 3.19,

f(x1,x2. x3) elsewhere

Find the joint marginal density of X₁ and X₃ and the marginal density of X₁ alone.

f(x1,x2. x3) elsewhere

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