a) Suppose that the joint density function of two random variables W, and W, is giv by f(w₁, W₂) = {c(w₁ + w₂ w²), 0, 0

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a) Suppose that the joint density function of two random variables W, and W, is giv
by
f(W₂, W₂) = {C(W₁ + w₂),
0.
i) Find P (W₁ < ≥ |W₂ < 1).
ii) Find cov(W₁, W₂).
iii) Show whether or not W₁ and W₂ are independent.
b) Suppose that the joint density function of random variables X₁ and X₂ is given by
f(x₁, x₂) = 2
0<w₁ <1,0 <W₂ <2
elsewhere
0,
0 < x, < x₂ < 2
otherwise
i) Draw a sketch of the area where f(x₁, x₂) is not zero.
ii) Find P(X₂ < 1).
iii) Find E(X₁X₂).
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Transcribed Image Text:a) Suppose that the joint density function of two random variables W, and W, is giv by f(W₂, W₂) = {C(W₁ + w₂), 0. i) Find P (W₁ < ≥ |W₂ < 1). ii) Find cov(W₁, W₂). iii) Show whether or not W₁ and W₂ are independent. b) Suppose that the joint density function of random variables X₁ and X₂ is given by f(x₁, x₂) = 2 0<w₁ <1,0 <W₂ <2 elsewhere 0, 0 < x, < x₂ < 2 otherwise i) Draw a sketch of the area where f(x₁, x₂) is not zero. ii) Find P(X₂ < 1). iii) Find E(X₁X₂). HUAWEI P smart 2021 48MP QUAD CAMERA AI
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