Show that random variables X and Y are not independent if the joint density function is...

Question

Question

Answer 1

Answer #1

Sels. The joint denisity function of t and y frit) = ungurys ne de (y +1) The marginal density of x . fx C) = f for middy = 8

Answer 2

Similar Homework Help Questions

The joint probability density function for continuous random variables X and Y is given below. f...

The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...
The joint probability density function for continuous random variables X and Y is given below. f...

The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...
The joint probability density function for continuous random variables X and Y is given below. f...

The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...

Exercise 6.55 Let X and Y be random variables with joint density function f(x, y)- 4 0 otherwise ...

Exercise 6.55 Let X and Y be random variables with joint density function f(x, y)- 4 0 otherwise Show that the joint density function of U = 3(X-Y) and V = Y is otherwise, where A is a region of the (u, v) plane to be determined. Deduce that U has the bilateral exponential distribution with density function fu (11) te-lul foru R. Exercise 6.55 Let X and Y be random variables with joint density function f(x, y)- 4 0...
Suppose X and Y are jointly continuous random variables with joint density function Let U =...

Suppose X and Y are jointly continuous random variables with joint density function Let U = 2X − Y and V = 2X + Y (i). What is the joint density function of U and V ? (ii). Calculate Var(U |V ). 1. Suppose X and Y are jointly continuous random variables with join density function Lei otherwise Let U = 2X-Y and V = 2X + y (i). What is the joint density function of U and V? (ii)....
2. Suppose that the random variables X and Y have joint probability density function given by...

2. Suppose that the random variables X and Y have joint probability density function given by f(x, y) = 18(x - x?)y?, 0SX S1, OS y si. Let U = XY. Find the density function of U.

The joint distribution function for two random variables X and Y is Fxx(x,y) = u(x) u(y)[1...

The joint distribution function for two random variables X and Y is Fxx(x,y) = u(x) u(y)[1 - e-ax - e-av + e-a(x+y)], where a>0 Find and sketch the marginal pdf fyly)
8), Let X and Y be continuous random variables with joint density function f(x,y)-4xy for 0...

8), Let X and Y be continuous random variables with joint density function f(x,y)-4xy for 0 < x < y < 1 Otherwise What is the joint density of U and V Y
Consider the following joint probability density function of the random variables X and Y : (a)...

Consider the following joint probability density function of the random variables X and Y : (a) Find its marginal density functions (b) Are X and Y independent? (c) Find the condition density functions . (d) Evaluate P(0<X<2|Y=1)

The joint probability density function of the random variables X, Y, and Z is (e-(x+y+z) f(x,...

The joint probability density function of the random variables X, Y, and Z is (e-(x+y+z) f(x, y, z) 0 < x, 0 < y, 0 <z elsewhere (a) (3 pts) Verify that the joint density function is a valid density function. (b) (3 pts) Find the joint marginal density function of X and Y alone (by integrating over 2). (C) (4 pts) Find the marginal density functions for X and Y. (d) (3 pts) What are P(1 < X <...