Question

The continuous random variables X and Y have joint pdf f(x, y) = cy2 + xy/3   0...

The continuous random variables X and Y have joint pdf f(x, y) = cy2 + xy/3   0 ≤ x ≤ 2, 0 ≤ y ≤ 1 (a) What is the value of c that makes this a proper pdf? (b) Find the marginal distribution of X. (c) (4 points) Find the marginal distribution of Y . (d) (3 points) Are X and Y independent? Show your work to support your answer.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

please rate me high.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose X and Y are continuous random variables with joint pdf f(x,y) = 2(x+y) if 0...
Suppose X and Y are continuous random variables with joint pdf f(x,y) = 2(x+y) if 0 < x < < y < 1 and 0 otherwise. Find the marginal pdf of T if S=X and T = XY. Use the joint pdf of S = X and T = XY.
Suppose the continuous random variables X and Y have joint pdf: fXY (x, y) = （1/2）xy...
Suppose the continuous random variables X and Y have joint pdf: fXY (x, y) = （1/2）xy for 0 < x < 2 and x < y < 2 (a) Find P(X < 1, Y < 1). (b) Use the joint pdf to find P(Y > 1). Be careful setting up your limits of integration. (c) Find the marginal pdf of Y , fY (y). Be sure to state the support. (d) Use the marginal pdf of Y to find P(Y...
19. Let X and Y be continuous random variables with joint pdf: f(x, y) = x−y...
19. Let X and Y be continuous random variables with joint pdf: f(x, y) = x−y for 0 ≤ y ≤ 1 and 1 ≤ x ≤ 2. If U = XY and V = X/Y , calculate the joint pdf of U and V , fUV (u, v).
Suppose the continuous random variables X and Y have joint pdf: fXY (x, y) = （1/2）xy...
Suppose the continuous random variables X and Y have joint pdf: fXY (x, y) = （1/2）xy for 0 < x < 2 and x < y < 2 (a) Find P(Y < 2X) by integrating in the x direction first. Be careful setting up your limits of integration. (b) Find P(Y < 2X) by integrating in the y direction first. Be extra careful setting up your limits of integration. (c) Find the conditional pdf of X given Y = y,...
4. Let X and Y be random variables having joint probability density function (pdf) f(x, y)...
4. Let X and Y be random variables having joint probability density function (pdf) f(x, y) = 4/7 (xy − y), 4 < x < 5 and 0 < y < 1 (a) Find the marginal density fY (y). (b) Show that the marginal density, fY (y), integrates to 1 (i.e., it is a density.) (c) Find fX|Y (x|y), the conditional density of X given Y = y. (d) Show that fX|Y (x|y) is actually a pdf (i.e., it integrates...
Suppose X and Y are continuous random variables with joint pdf f(x,y) = x + y,...
Suppose X and Y are continuous random variables with joint pdf f(x,y) = x + y, 0 < x< 1, 0 < y< 1. Let W = max(X,Y). Find EW.
Consider continuous random variables X and Y whose joint pdf is f(x, y) = 1 with...
Consider continuous random variables X and Y whose joint pdf is f(x, y) = 1 with 0 < y < 1 − |x|. Show that Cov(X, Y ) = 0 even though X and Y are dependent. Note: For this problem, you only need to show that the covariance is zero. You need not show that X and Y are dependent.
Consider continuous random variables X and Y whose joint pdf is f(x, y) = 1 with...
Consider continuous random variables X and Y whose joint pdf is f(x, y) = 1 with 0 < y <1 – abs(x). Show that Cov(X, Y ) = 0 even though X and Y are dependent. Note: For this problem, you only need to show that the covariance is zero. You need not show that X and Y are dependent.
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...
Let X and Y be random variables with the joint pdf fX,Y(x,y) = 6x, 0 ≤...
Let X and Y be random variables with the joint pdf fX,Y(x,y) = 6x, 0 ≤ y ≤ 1−x, 0 ≤ x ≤1. 1. Are X and Y independent? Explain with a picture. 2. Find the marginal pdf fX(x). 3. Find P( Y < 1/8 | X = 1/2 )
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT