Suppose X andY have joint density f(x,y)=6xy^2 for 0<x<1, 0<y<1. (a) What is P(X+Y ≤1)? (b)...

Question

Question

Suppose X andY have joint density f(x,y)=6*x*y^2 for 0<x<1, 0<y<1.

(a) What is P(X+Y ≤1)?
(b) Compute the marginal densities fX , fY of X, Y .

Answer 1

Answer #1

SU co pro nalry €0 PextY51)- 5fins daly la age incly ( [ar 27 day afby? (13° dy = 3 1/4 = (1-29792) dy +33stway+94 dy » 3 (?

Answer 2

Similar Homework Help Questions

1. (20 pts) RVs X and Y have joint density function 22 f(x, y) =(0 if O <z<1 and 0<y<2 īf 0 < x < 1 and 0 < y < 2 otherwise (a) Find E(X), V(X), E(Y), and V(Y). (b) Find t...

1. (20 pts) RVs X and Y have joint density function 22 f(x, y) =(0 if O <z<1 and 0<y<2 īf 0 < x < 1 and 0 < y < 2 otherwise (a) Find E(X), V(X), E(Y), and V(Y). (b) Find the covariance cov(X,Y) and the associated correlation ρ (c) Find the marginal densities fx and fy. (Be sure to say where they're nonzero.) (d) Find E(X | Y = 1.5). (e) Are X and Y independent? Give two...
4. Suppose X and Y has joint density f(x, y) = 2 for () < x...

4. Suppose X and Y has joint density f(x, y) = 2 for () < x <y<1. (a) Find P(Y - X > 2). (b) Find the marginal densities of X and Y. (c) Find E(X), E(Y), Var(X), Var(Y), Cov(X,Y)
4. Suppose that a two-dimensional random vector (X, Y) has a joint probability density function as 0.48y(2-x), 0 1,...

4. Suppose that a two-dimensional random vector (X, Y) has a joint probability density function as 0.48y(2-x), 0 1,0 x y x f(x,y)- 0, otherwise Find two possible marginal probability functions fx(x) and fy(y) of X and Y, respectively. 4. Suppose that a two-dimensional random vector (X, Y) has a joint probability density function as 0.48y(2-x), 0 1,0 x y x f(x,y)- 0, otherwise Find two possible marginal probability functions fx(x) and fy(y) of X and Y, respectively.

[15] 5. (X, Y) have joint density (22 + y?) 0<*<1 0<y<1 f(x, y) else find...

[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).
The joint density of random variables X and Y is given to be f(x,y) =xy^2 for 0≤x≤y≤1 and is 0 el...

The joint density of random variables X and Y is given to be f(x,y) =xy^2 for 0≤x≤y≤1 and is 0 elsewhere. (a) Compute the marginal densities for X and for Y respectively. (b) Compute the expected valueE(XY). (c) Define a new random variable W=Y/X. Compute the probability P(W > t) for anyt >1. Also find the probability P(W <1/2) ?
2. Let X and Y have joint density f(x.v) = \ şcy? if 0 <x< 1...

2. Let X and Y have joint density f(x.v) = \ şcy? if 0 <x< 1 and 1 <y<2, otherwise. (a) Compute the marginal probability density function of Y. If it's equal to 0 outside of some range, be sure to make this clear. (b) Set up but do not compute an integral to find P(Y < 2X).

4. Let X and Y have joint probability density function f(x,y) = 139264 oray3 if 0...

4. Let X and Y have joint probability density function f(x,y) = 139264 oray3 if 0 < x, y < 4 and y> 4-1, otherwise. (a) Set up but do not compute an integral to find E(XY). (b) Let fx() be the marginal probability density function of X. Set up but do not compute an integral to find fx(x) when I <r54. (c) Set up but do not compute an integral to find P(Y > X).
The joint density of X and Y is given as f(x, y) = 4xy, 0 <...

The joint density of X and Y is given as f(x, y) = 4xy, 0 < x, 1 and 0 < y < 1. (a). Find the marginal distribution of Y, fY (y). (b). Find E[X|Y = 1/2]. (c). Find P(X < .3|Y < .2).
2.8.14 Let X and Y have joint density fX,Y (x, y) = (x2 + y)/36 for...

2.8.14 Let X and Y have joint density fX,Y (x, y) = (x2 + y)/36 for −2 < x < 1 and 0 < y < 4, otherwise fX,Y (x, y) = 0. (a) Compute the conditional density fY|X (y|x) for all x, y ∈ R1 with fX (x) > 0. (b) Compute the conditional density fX|Y (x|y) for all x, y ∈ R1 with fY (y) > 0. (c) Are X and Y independent? Why or why not?

4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x <...

4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x < y < 1, and zero otherwise. (a) Find fx(x). (b) Find fy(y). (c) Find Corr(X,Y). (d) Find fy x(y|x). (e) Find E(Y|X). (f) Find Var(Y). (g) Find Var(E(Y|X)). (h) Find E (Var(Y|X)]. (i) Find the pdf of Y - X.

Suppose X andY have joint density f(x,y)=6*x*y^2 for 0<x<1, 0<y<1. (a) What is P(X+Y ≤1)? (b)...