please explain each step 5.21 Let X and Y be independent random variables with fae-ax, x>0...
4.5.4 X and Y are random variables with the joint PDF ( 5x2/2 JX,Y (x, y) = -1 < x < 1; 0 <y < x2, otherwise. 10 (a) What is the marginal PDF fx(x)? (6) What is the marginal PDF fy(y)?
5.5.5 X and Y are random variables w the joint PDF X,Y (z, y) = 0 otherwise. (a) What is the marginal PDF fx()? (b) What is the marginal PDF fr(v)?
Question 3 [17 marks] The random variables X and Y are continuous, with joint pdf 0 y otherwise ce fxx (,y) a) Show that cye fr (y) otherwise and hence that c = 1. What is this pdf called? (b) Compute E (Y) and var Y; (c) Show that { > 0 fx (a) e otherwise (d) Are X and Y independent? Give reasons; (e) Show that 1 E(XIY 2 and hence show that E (XY) =. Question 3 [17...
Let X and Y be random variables with joint PDF fx,y(x, y) = 2 for 0 < y < x < 1. Find Var(Y|X).
Let X and Y be continuous random variables with joint pdf f(x,y) =fX (c(X + Y), 0 < y < x <1 otBerwise a. Find c. b. Find the joint pdf of S = Y and T = XY. c. Find the marginal pdf of T. 、
(6 points) Let X and Y be independent random variables with p.d.f.s fx(x) -{ { 1-22 0, for |2|<1, otherwise. fy(y) = for y>0, otherwise. 0, Let W = XY (a) (2 points) Find the p.d.f. of W, fw(w). (b) (2 points) Find the moment generating function of W2, Mw?(t) = E (e«w?). (c) (2 points) Find the conditional expectation of W given Y = y, E(W|Y = y).
Random variables z and y described by the PDF if x-+ yo 1 and x.> 0 and y, > 0 0 otherwise a Are x and y independent random variables? b Are they conditionally independent given max(x,y) S 0.5? c Determine the expected value of random variabler, defined byr xy.
Let X and Y be continuous random variables with following joint pdf f(x, y): y 0<1 and 0<y< 1 0 otherwise f(x,y) = Using the distribution method, find the pdf of Z = XY.
Thank you! Q8 Consider two independent continuous random variables X and Y with probability density function given as follows: fx(x) 1/10, 0<x< 10 0 otherwise 0y 10 fro-6/10, (y) = Enter all answers as a fraction (e.g. 4/5) or integer. a. Create the joint pdf from the marginals: <<y<0 otherwise. Submit Answer Tries 0/15 b, Find E(X 1 Y 2) Submit Answer Tries 0/5 C. Find E(Y 1 X = 2) Submit Answer Tries 0/5 d. Find Cov(X, Y) Submit...
7. The joint pdf of two random variables X and Y is given by 0sxs3,0s y<5 fx(x,y) 15' 0, otherwise Find Cov(X,y)