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, p_X and p_Y. 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, f_X and f_Y. Provide a formula, analogous to the one in part (a), for f_Z|Y(z|y) in terms of f_X. That is, find A and B in the formula below.
f_Z|Y(z|y)=Af_X(B).

A=

B=

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

f_Z(z)=…
(Choose all that apply.)

to see the options :
I[dot]imgur[dot]com/WQOtsyh.jpg

Answer 1

1. z*y

2. A = ?
B = ?

3. Option 4