Question 3: Independent or not? For the following four joint probability distributions of X and Y...

Question 3: Independent or not? For the following four joint probability distributions of X and Y , either prove or disprove that X and Y are independent. 1. fXY (x, y) = λ 2 e −λ(x+y) , x, y ≥ 0. 2. fXY (x, y) = 6 5 x + y 2 , 0 ≤ x, y ≤ 1. 3. fXY (x, y) = 1 9 xy, 0 ≤ x ≤ 3, and 0 ≤ y ≤ 2. 4. fXY (x, y) = 8xy, 0 ≤ x ≤ y ≤ 1.

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Question 3: Independent or not? For the following four joint probability distributions of X and Y...

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