Question

Let X and Y be a random variables with the joint probability density function fX,Y (x,...

Let X and Y be a random variables with the joint probability density function fX,Y (x, y) = { cx2y, 0 < x2 < y < x for x > 0 0, otherwise }. compute the marginal probability density functions fX(x) and fY (y). Are the random variables X and Y independent?.

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

Homework Answers

Answer #1

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
Let fX,Y be the joint density function of the random variables X and Y which is...
Let fX,Y be the joint density function of the random variables X and Y which is equal to fX,Y (x, y) = { x + y if 0 < x, y < 1, 0 otherwise. } Compute the probability density function of X + Y . Referring to the problem above, compute the marginal probability density functions fX(x) and fY (y). Are the random variables X and Y independent?
Let X and Y be a random variables with the joint probability density function fX,Y (x,...
Let X and Y be a random variables with the joint probability density function fX,Y (x, y) = { e −x−y , 0 < x, y < ∞ 0, otherwise } . a. Let W = max(X, Y ) Compute the probability density function of W. b. Let U = min(X, Y ) Compute the probability density function of U. c. Compute the probability density function of X + Y .
For continuous random variables X and Y with joint probability density function. f(x,y) = xe−(x+y) when...
For continuous random variables X and Y with joint probability density function. f(x,y) = xe−(x+y) when x > 0 and y > 0 f(x,y) = 0 otherwise a. Find the conditional density F xly (xly) b. Find the marginal probability density function fX (x) c. Find the marginal probability density function fY (y). d. Explain if X and Y are independent
Let X and Y be continuous random variables with joint density function f(x,y) and marginal density...
Let X and Y be continuous random variables with joint density function f(x,y) and marginal density functions fX(x) and fY(y) respectively. Further, the support for both of these marginal density functions is the interval (0,1). Which of the following statements is always true? (Note there may be more than one)    E[X^2Y^3]=(∫0 TO 1 x^2 dx)(∫0 TO 1 y^3dy)    E[X^2Y^3]=∫0 TO 1∫0 TO 1x^2y^3 f(x,y) dy dx    E[Y^3]=∫0 TO 1 y^3 fX(x) dx   E[XY]=(∫0 TO 1 x fX(x)...
A joint density function is given by fX,Y (x, y) = ( kx, 0 < x...
A joint density function is given by fX,Y (x, y) = ( kx, 0 < x < 1, 0 < y < 1 0, otherwise. (a) Calculate k (b) Calculate marginal density function fX(x) (c) Calculate marginal density function fY (y) (d) Compute P(X < 0.5, Y < 0.1) (e) Compute P(X < Y ) (f) Compute P(X < Y |X < 0.5) (g) Are X and Y independent random variables? Show your reasoning (no credit for yes/no answer). (h)...
Let X and Y have the joint probability density function f(x, y) = ⎧⎪⎪ ⎨ ⎪⎪⎩...
Let X and Y have the joint probability density function f(x, y) = ⎧⎪⎪ ⎨ ⎪⎪⎩ ke−y , if 0 ≤ x ≤ y < ∞, 0, otherwise. (a) (6pts) Find k so that f(x, y) is a valid joint p.d.f. (b) (6pts) Find the marginal p.d.f. fX(x) and fY (y). Are X and Y independent?
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...
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 given by fX,Y...
The joint probability density function of two random variables (X and Y) is given by fX,Y (x, y) = ( C √y (y ^(α+1)) exp {( − y(2β+x ^2 ) )/2 } , x ∈ (−∞,∞), y ∈ [0,∞), 0 otherwise. (a) Find C. (b) Find the marginal density of Y . What type of distribution does Y follow? (c) Find the conditional density of X | Y . What type of distribution is this?
Consider the random variables X and Y with the following joint probability density function: fX,Y (x,...
Consider the random variables X and Y with the following joint probability density function: fX,Y (x, y) = xe-xe-y, x > 0, y > 0 (a) Suppose that U = X + Y and V = Y/X. Express X and Y in terms of U and V . (b) Find the joint PDF of U and V . (c) Find and identify the marginal PDF of U (d) Find the marginal PDF of V (e) Are U and V independent?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT