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

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a) Suppose that the joint density function of two random variables W₁ and W₂ is given
by
f(w₁, W₂) = {c(W₁
+ w²), 0<w₁ <1,0 <w₂ < 2
0,
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:a) Suppose that the joint density function of two random variables W₁ and W₂ is given by f(w₁, W₂) = {c(W₁ + w²), 0<w₁ <1,0 <w₂ < 2 0, 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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