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

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 21CR
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7.

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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