Question: Setup: Let X and Y be independent positive random variables. Let Z = X|Y . In what follows, all occurrences of x, y, z are

Setup:

LetX andY be independent positive random variables. LetZ = X|Y. In what follows, all occurrences ofx, y, zare assumed to be positive numbers.

Question:

Which of the following is a formula for?_Z(z) ?

?_Z(z)=...

(Choose all that apply.)

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Setup:LetX andY be independent positive random variables. LetZ = X|Y. In what

follows, all occurrences ofx, y, zare assumed to be positive numbers.Question:Which of

Let X and Y be independent positive random variables. Let Z = X/Y . In what follows, all occurrences of x, y, z are assumed to be positive numbers. 1. Suppose that X and Y are discrete, with known PMFs, px and py. Then, PZIY (z | y) = Px (?). What is the argument in the place of the question mark? 2. Suppose that X and Y are continuous, with known PDFs, fx and fy. Provide a formula, analogous to the one in part (a), for fzy (z | y) in terms of fx. That is, find A and B in the formula below. fzx (zly) = A fx (B) . A = B = 3. Which of the following is a formula for fz (z)?3. Which of the following is a formula for fz (z)? fz ( z) = ... (Choose all that apply.) f z ( 2 ) = fy,z (y, z) dy Ofz (2) = fy,z (y, z) dz Ofz (2 ) = fx (y) fz,x ( z,y) dy Ofz ( 2) = | fx ( v) fzy ( zly) dy 00 Ofz (2 ) = | fy ( v) fx ( yz) dy 0O yfy ( y) fx ( yz) dy

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