Question

Given :  f(x,y)=6x, 0<x<1,0<y<1−x Find: marginal pdf’s for X and Y, conditional pdf’s, P(0 < X <...

Given :  f(x,y)=6x, 0<x<1,0<y<1−x

Find: marginal pdf’s for X and Y, conditional pdf’s, P(0 < X < 0.5,0 < Y < 0.25), E(X), and V(X)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Let (X,Y ) be a pair of random variables with joint pdf given by f(x,y)...
1. Let (X,Y ) be a pair of random variables with joint pdf given by f(x,y) = 1(0 < x < 1,0 < y < 1). (a) Find P(X + Y ≤ 1). (b) Find P(|X −Y|≤ 1/2). (c) Find the joint cdf F(x,y) of (X,Y ) for all (x,y) ∈R×R. (d) Find the marginal pdf fX of X. (e) Find the marginal pdf fY of Y . (f) Find the conditional pdf f(x|y) of X|Y = y for 0...
Suppose the random variable (X, Y ) has a joint pdf for the form ?cxy 0≤x≤1,0≤y≤1...
Suppose the random variable (X, Y ) has a joint pdf for the form ?cxy 0≤x≤1,0≤y≤1 f(x,y) = . 0 elsewhere (a) (5 pts) Find c so that f is a valid distribution. (b) (6 pts) Find the marginal distribution, g(x) for X and the marginal distribution for Y , h(y). (c) (6 pts) Find P (X > Y ). (d) (6 pts) Find the pdf of X +Y. (e) (6 pts) Find P (Y < 1/2|X > 1/2). (f)...
Let X and Y have a joint density function given by f(x; y) = 3x; 0...
Let X and Y have a joint density function given by f(x; y) = 3x; 0 <= y <= x <= 1 (a) Find P(X<2Y). (b) Find cov(X,Y). (c) Find P(X < 1/2 |Y = 1/3). (d) Find P(X = 1/2|Y = 1/3). (e) Find P(X > 1/2|Y > 1/3). (f) Find the conditional expectation E(X|Y = y).
Given f''(x)=−36sin(6x) and f'(0)=1 and f(0)=−2 . Find f(π/6) =
Given f''(x)=−36sin(6x) and f'(0)=1 and f(0)=−2 . Find f(π/6) =
Given the joint probability density function f ( x , y ) for 0 < x...
Given the joint probability density function f ( x , y ) for 0 < x < 3 and 0 < y < 2 x^2y/81 Find the conditional probability distribution of X=1 given that Y = 1 f ( x , y ) = x^2 y/ 81 . F i n d the conditional probability distribution of X=1 given that Y = 1. i . e . f (X ∣ y = 1 )( 1 )
Given a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5...
Given a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5 0.25 Define Y = X2 & W= Y+2. Which one of the following statements is not true? A) V[Y] = 0.25. B) E[XY] = 0. C) E[X3] = 0. D) E[X+2] = 2. E) E[Y+2] = 2.5. F) E[W+2] = 4.5. G) V[X+2] = 0.5. H) V[W+2] = 0.25. I) P[W=1] = 0.5 J) X and W are not independent.
Given a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5...
Given a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5 0.25 Define Y = X2 & W= Y+2. Which one of the following statements is not true? A) V[Y] = 0.25. B) E[XY] = 0. C) E[X3] = 0. D) E[X+2] = 2. E) E[Y+2] = 2.5. F) E[W+2] = 4.5. G) V[X+2] = 0.5. H) V[W+2] = 0.25. I) P[W=1] = 0.5 J) X and W are not independent.
Let X and Y be two continuous random variables with joint probability density function f(x,y) =...
Let X and Y be two continuous random variables with joint probability density function f(x,y) = 6x 0<y<1, 0<x<y, 0 otherwise. a) Find the marginal density of Y . b) Are X and Y independent? c) Find the conditional density of X given Y = 1 /2
The joint probability density function of two random variables X and Y is f(x, y) =...
The joint probability density function of two random variables X and Y is f(x, y) = 4xy for 0 < x < 1, 0 < y < 1, and f(x, y) = 0 elsewhere. (i) Find the marginal densities of X and Y . (ii) Find the conditional density of X given Y = y. (iii) Are X and Y independent random variables? (iv) Find E[X], V (X) and covariance between X and Y .
X and Y are jointly continuous with joint pdf f(x, y) = 2, x > 0,...
X and Y are jointly continuous with joint pdf f(x, y) = 2, x > 0, y > 0, x + y ≤ 1 and 0 otherwise. a) Find marginal pdf’s of X and of Y. b) Find covariance Cov(X,Y). c) Find correlation Corr(X,Y). What you can say about the relationship between X and Y?