Let X and Y be random variables with joint density function, f(x, y) = e¯ª,0. If Z = X + 2Y and W = X. Which of the following is true? (A). The joint PDF of W and Z is e-w, and W and Z are independent (B.) The joint PDF of W and Z is e-w, and W and Z are independent (C) The joint PDF of W and Z is te-", and W and Z are dependent (D.) The joint PDF of W and Z is e-w, and W and Z are dependent

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Let X and Y be random variables with joint density
function,
f(x, y) = e-, 0. If Z = X + 2Y and W = X.
Which of the following is true?
(A). The joint PDF of W and Z is e-w, and W and
Z are independent
(B.) The joint PDF of W and Z is e-w, and W and Z
are independent
(C) The joint PDF of W and Z is te-", and W and Z
are dependent
(D.) The joint PDF of W and Z is e-w, and W and Z
are dependent
В
O A
ос
Transcribed Image Text:Let X and Y be random variables with joint density function, f(x, y) = e-, 0. If Z = X + 2Y and W = X. Which of the following is true? (A). The joint PDF of W and Z is e-w, and W and Z are independent (B.) The joint PDF of W and Z is e-w, and W and Z are independent (C) The joint PDF of W and Z is te-", and W and Z are dependent (D.) The joint PDF of W and Z is e-w, and W and Z are dependent В O A ос
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