Hello, please answer my question. Thanks

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, PZY (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 (zly) in terms of fx. That is, find A and B in the formula below. fzy ( zly) = Afx (B) . A = B =3. Which of the following is a formula for fz (z)? f z ( 2) =... (Choose all that apply.) f z ( 2 ) = ] fx,z (y, 2 ) dy fz ( z ) = fy,z (y, z) dz fz ( z) = fy (y) fz,x (z,y) dy fz (2) = fy (y) fzy (zly) dy fz ( 2 ) = / fx (3 ) fx (yz ) dy f z ( z ) = yfy (y) fx (yz) dyProblem 4(a) 2 points possible (graded, results hidden) A random variable X is generated as follows. We flip a coin. With probability p, the result is Heads, and then X is generated according to a PDF fx|H which is uniform on [0, 1]. With probability 1 - p the result is Tails, and then X is generated according to a PDF fxIT of the form fXT (2) = 2x, if x E [0, 1] . (The PDF is zero everywhere else.) 1. What is the (unconditional) PDF fx (a) of X? For 0 a. What is a? a =Problem 3 2.5 points possible (graded, results hidden) Let X be uniform on 0, 1 /2) . Find the PDF fy (y) of Y = X/ (1 - X). For 0