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.

Question

1) Suppose that X and Y are discrete, with known PMFs, pX and pY . Then,

pZ|Y(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 fZ|Y(z|y) in terms of fX . That is, find A and B in the formula below.

fZ|Y(z|y)=AfX(B).

A= ?

B= ?

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

fZ(z)=…
(Choose all that apply.)

a) fZ(z)=∫∞0fY,Z(y,z)dy
b) fZ(z)=∫∞0fY,Z(y,z)dz
c) fZ(z)=∫∞0fY(y)fZ,Y(z,y)dy
d) fZ(z)=∫∞0fY(y)fZ|Y(z|y)dy
e) fZ(z)=∫∞0fY(y)fX(yz)dy
f) fZ(z)=∫∞0yfY(y)fX(yz)dy

Answer 1

Check the last option in 3). You can find all answers here.

a,d,f

Answer 2

I am still lost here. Can anyone give me a hint?

Answer 3

www.jiskha.com/questions/1822154/let-and-be-independent-positive-random-variables-let-in-what