6. (5 marks) The joint density of X and Y is given as 0, else Find...
6. (5 marks) The joint density of X and Y is given as 0, else Find the probability density function of U-Y/X. Use any method you wish
3. (5 marks) The joint density of X and Y is given as else Find the probability density function of U-X-Y.
1. (15 marks) The joint density of X and Y is given as f(x.))-o, else a) (5 marks) Find the probability density function of W-Y", where a>0 b) (5 marks) Find the probability density function of U- XY 0(5 marks) Find the probability density function of V-X-Y
Use the Method of Distribution Functions 3. (5 marks) The joint density of X and Y is given as , else Use the Method of Distribution Functions Find the probability density function of U- X-Y.
Use Multivariate Transformations 7. (10 marks) The joint density of X and Y is given as f(x,y)=10, else a) (5 marks) Find the joint probability density function of = X / y and V = X. b) (5 marks) Using your result in (a), find the marginal density of V.
Use the method of distribution functions 3. (5 marks) The joint density ofX and Y is given as 0 , else Find the probability density function of UX-Y.
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find the marginal probability density function of Y and identify its distribution. (5 marks (b) Find the conditional probability density function of X given Y=y and hence find the mean and variance of X conditional on Y=y. [7 marks] (c) Use iterated expectation to find the expected value of X [5 marks (d) Use E(XY) and var(XY) from (b) above to find the variance of...
Question 1(a&b) Question 3 (a,b,c,d) QUESTION 1 (15 MARKS) Let X and Y be continuous random variables with joint probability density function 6e.de +3,, х, у z 0 otherwise f(x, y 0 Determine whether or not X and Y are independent. (9 marks) a) b) Find P(x> Y). Show how you get the limits for X and Y (6 marks) QUESTION 3 (19 MARKS) Let f(x, x.) = 2x, , o x, sk: O a) Find k xsl and f(x,...
4. The random variables X and Y have joint probability density function fx.y(r, y) given by: else (a) Find c (b) Find fx (r) and fr (u), the marginal probability density functions of X and Y, respectively (c) Find fxjy (rly), the conditional probability density function of X given Y. For your limits (which you should not forget!), put y between constant bounds and then give the limits for r in terms of y. (d) Are X and Y independent?...
[15] 5. (X, Y) have joint density (22 + y?) 0<*<1 0<y<1 f(x, y) else find the marginals fx(x) and fy (y).