Question

X and Y are continuous random variables. Their joint probability distribution function is : f(x,y) =...

X and Y are continuous random variables. Their joint probability distribution function is :

f(x,y) = 1/5(y+2) , 0 < y < 1, y-1 < x < y +1

= 0, otherwise

a) Find marginal density of Y, fy(y)

b) Calculate E[X | Y = 0]

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
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 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
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) = xe^−x(y+1), 0 , 0< x < ∞,0 < y < ∞ otherwise (a) Are X and Y independent or not? Why? (b) Find the conditional density function of Y given X = 1.(
X and Y are continuous random variables. Their joint probability density function is given as f(x,y)...
X and Y are continuous random variables. Their joint probability density function is given as f(x,y) = 1/5 (y+2) for 0<y<1 and y-1<x<y+1. Calculate the conditional expectation E(x/y=0). Please show all the work and explain if the answer will be a number or just y in a given range.
Let X and Y be jointly continuous random variables with joint density function f(x, y) =...
Let X and Y be jointly continuous random variables with joint density function f(x, y) = c(y^2 − x^2 )e^(−2y) , −y ≤ x ≤ y, 0 < y < ∞. (a) Find c so that f is a density function. (b) Find the marginal densities of X and Y . (c) Find the expected value of X
Suppose that the joint probability density function of the random variables X and Y is f(x,...
Suppose that the joint probability density function of the random variables X and Y is f(x, y) = 8 >< >: x + cy^2 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 0 otherwise. (a) Sketch the region of non-zero probability density and show that c = 3/ 2 . (b) Find P(X + Y < 1), P(X + Y = 1) and P(X + Y > 1). (c) Compute the marginal density function of X and Y...
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?.
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)...
Suppose that X1 and X2 are independent continuous random variables with the same probability density function...
Suppose that X1 and X2 are independent continuous random variables with the same probability density function as: f(x) = ( x 2 0 < x < 2, 0 otherwise. Let a new random variable be Y = min(X1, X2,). a) Use distribution function method to find the probability density function of Y, fY (y). b) Compute P(Y > 1). c) Compute E(Y )
A joint density function of the continuous random variables x and y is a function f(x,...
A joint density function of the continuous random variables x and y is a function f(x, y) satisfying the following properties. f(x, y) ≥ 0 for all (x, y) ∞ −∞ ∞ f(x, y) dA = 1 −∞ P[(x, y)  R] =    R f(x, y) dA Show that the function is a joint density function and find the required probability. f(x, y) = 1 8 ,   0 ≤ x ≤ 1, 1 ≤ y ≤ 9 0,   elsewhere P(0 ≤...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT