suppose that two random variables X and Y have joint Pdf, f(x,y) = 1/√2π * e^(-((x2y2)/2)-y)...

Question

Question

suppose that two random variables X and Y have joint Pdf,

f(x,y) = 1/√2π * e^(-((x²y²)/2)-y) * y² -inf < x < inf and y > 0

a) Are X and Y independent? Justify.

b) Find the distribution of Y

math Statistics-And-Probability

Answer 1

Answer #1

Here ,Y~Gamma(2,1) distribution,with shape=2 and scale=1

Answer 2

Similar Homework Help Questions

Suppose the joint pdf of random variables X and Y is f(x,y) = c/x, 0 <...

Suppose the joint pdf of random variables X and Y is f(x,y) = c/x, 0 < y < x < 1. a) Find constant c that makes f (x, y) a valid joint pdf. b) Find the marginal pdf of X and the marginal pdf of Y. Remember to provide the supports c) Are X and Y independent? Justify
4) The random variables X and Y have the joint PDF fx,y(x, y) = 0 <...

4) The random variables X and Y have the joint PDF fx,y(x, y) = 0 < x < 6,0 < y < 6 Find E [X2Y2].
5. Suppose that the joint pdf of the random variables X and Y is given by...

5. Suppose that the joint pdf of the random variables X and Y is given by - { ° 0 1, 0< y < 1 f (x, y) 0 elsewhere a) Find the marginal pdf of X Include the support b) Are X and Y independent? Explain c) Find P(XY < 1)

Two random variables have joint PDF of F(x, y) = 0 for x < 0 and...

Two random variables have joint PDF of F(x, y) = 0 for x < 0 and y < 0 for 0 <x< 1 and 0 <y<1 1. for x > 1 and y> 1 a) Find the joint and marginal pdfs. b) Use F(x, y) and find P(X<0.75, Y> 0.25), P(X<0.75, Y = 0.25), P(X<0.25)
4. Suppose that the joint pdf of the random variables X and Y is given by...

4. Suppose that the joint pdf of the random variables X and Y is given by f(x, y) = cx^2 + xy 3 , if 0 < x < 1, 0 < y < 2 0, otherwise. (a) Find the constant value (b) Find the marginal pdf of X. Include the support. (c) Find the conditional density function Y given X = x, i.e., f(y|x) (d) Find the conditional expectation E(Y |X = x). (e) Are X and Y independent?...
2. Suppose that Y and Y2 are continuous random variables with the joint probability density function...

2. Suppose that Y and Y2 are continuous random variables with the joint probability density function (joint pdf) a) Find k so that this is a proper joint pdf. b) Find the joint cumulative distribution function (joint cdf), FV1,y2)-POİ уг). Be y, sure it is completely specified! c) Find P(, 0.5% 0.25). d) Find P (n 292). e) Find EDY/ . f) Find the marginal distributions fiv,) and f2(/2). g) Find EM] and E[y]. h) Find the covariance between Y1...

1. Suppose X,Y are random variables whose joint pdf is given by f(x, y) = 1/...

1. Suppose X,Y are random variables whose joint pdf is given by f(x, y) = 1/ x , if 0 < x < 1, 0 < y < x f(x, y) =0, otherwise . Find the covariance of the random variables X and Y . 2.Let X1 be a Bernoulli random variable with parameter p1 and X2 be a Bernoulli random variable with parameter p2. Assume X1 and X2 are independent. What is the variance of the random variable Y...
1. Suppose X and Y are continuous random variables with joint pdf f(x,y) 4(z-xy) if =...

1. Suppose X and Y are continuous random variables with joint pdf f(x,y) 4(z-xy) if = 0 < x < 1 and 0 < y < 1, and zero otherwise. (a) Find E(XY) b) Find E(X-Y) (c) Find Var(X - Y) (d) What is E(Y)?
Two random variables have the joint density funcitn as follows: f(x,y)=x/y^2 , 0<x<y, 0<y<2 f(x,y)= 0,...

Two random variables have the joint density funcitn as follows: f(x,y)=x/y^2 , 0<x<y, 0<y<2 f(x,y)= 0, elsewhere a) Find the marginal distribution of X b)Find the marginal distribution of Y c)Are X and Y statistically independent? (Justify your answer.) d) Find f(x/y)

Two random variables, X and Y, have joint probability density function f ( x , y...

Two random variables, X and Y, have joint probability density function f ( x , y ) = { c , x < y < x + 1 , 0 < x < 1 0 , o t h e r w i s e Find c value. What's the conditional p.d.f of Y given X = x, i.e., f Y ∣ X = x ( y ) ? Don't forget the support of Y. Find the conditional expectation E [...