Suppose that the joint density function of two random variables W₁ and W₂ is given by f(w₁, ₂) = {C(W₁ + ²), 0, 0

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Suppose that the joint density function of two random variables W₁ and W₂ is given
by
F (w₁, W₂) = {C(W₁ + w?),
0,
0<w₁ <1,0 <W₂ <2
elsewhere
i) Find P (W₁ <¹W₂ < 1).
ii) Find cov(W₁, W₂).
iii) Show whether or not W₁ and W₂ are independent.
Transcribed Image Text:Suppose that the joint density function of two random variables W₁ and W₂ is given by F (w₁, W₂) = {C(W₁ + w?), 0, 0<w₁ <1,0 <W₂ <2 elsewhere i) Find P (W₁ <¹W₂ < 1). ii) Find cov(W₁, W₂). iii) Show whether or not W₁ and W₂ are independent.
Suppose that the joint density function of two random variables W₁ and W₂ is given
by
F (w₁, W₂) = {C(W₁ + w?),
0,
0<w₁ <1,0 <W₂ <2
elsewhere
i) Find P (W₁ <¹W₂ < 1).
ii) Find cov(W₁, W₂).
iii) Show whether or not W₁ and W₂ are independent.
Transcribed Image Text:Suppose that the joint density function of two random variables W₁ and W₂ is given by F (w₁, W₂) = {C(W₁ + w?), 0, 0<w₁ <1,0 <W₂ <2 elsewhere i) Find P (W₁ <¹W₂ < 1). ii) Find cov(W₁, W₂). iii) Show whether or not W₁ and W₂ are independent.
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