1. Let X 1 and X 2 have the joint pdf f(x 1 , x 2 ) = 15x 2 1 x 2 , 0 1 2 1 + X 2 ≤ 1). Hint: Graph the space X 1 and X 2 and carefully choose the limits of integration in determining each marginal...

1. Let X₁
and X₂
have the joint pdf f(x₁, x₂) = 15x²
₁x₂, 0
_1
2
<>₁
+ X₂
≤ 1). Hint: Graph the space X₁
and X₂
and carefully choose the limits of integration in determining each marginal pdf.

2. Let X₁, X₂
be two random variables with the joint pmf p(x₁, x₂), (x₁, x₂) ∈ S, where S is the support of X₁, X₂. Let Y = g(X₁, X₂) be a function such that