(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf...

(i) Find the marginal probability distributions for the random variables X₁ and X₂ with joint pdf

f(x₁, x₂) = 12x₁x₂(1-x₂) , 0 < x₁ <1 0 < x₂ < 1

, otherwise

(ii) Calculate E(X₁) and E(X₂)

(iii) Are the variables X₁and X₂ stochastically independent?

(iv) Given the variables in the question, find the conditional p.d.f. of X₁ given 0<x₂< ½ and the conditional expectation E[X₁|0<x₂< ½ ].

Expert Solution

orchestra answered 1 year ago

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