Suppose that the joint density function of two random variables W₁ and W₂ is given by ƒ (w₁, w₂) = {C(W₁ + w₂), 0, 0

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7.THEORY OF DISTRIBUTIONS Statistics

Suppose that the joint density function of two random variables W₁ and W₂ is given
by
(c(W₁ + w²),
0,
ƒ(W₁, W₂) = {C(W₁ -
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 (c(W₁ + w²), 0, ƒ(W₁, W₂) = {C(W₁ - 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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