Question

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.

  1. f(x, y) ≥ 0 for all (x, y)

  2. ∞
    −∞
    ∞ f(x, y) dA = 1
    −∞
  3. 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 ≤ x ≤ 1, 1 ≤ y ≤ 7)

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 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.
a) The joint probability density function of the random variables X, Y is given as f(x,y)...
a) The joint probability density function of the random variables X, Y is given as f(x,y) = 8xy    if  0≤y≤x≤1 , and 0 elsewhere. Find the marginal probability density functions. b) Find the expected values EX and EY for the density function above c) find Cov  X,Y .
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
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
9. Suppose X and Y are continuous random variables with joint density function f(x,y) = x...
9. Suppose X and Y are continuous random variables with joint density function f(x,y) = x + y for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. (a). Compute the joint CDF F(x,y). (b). Compute the marginal density for X and Y . (c). Compute Cov(X,Y ). Are X and Y independent?
Suppose X and Y are continuous random variables with joint density function f(x,y) = x +...
Suppose X and Y are continuous random variables with joint density function f(x,y) = x + y for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. (a). Compute the joint CDF F(x,y). (b). Compute the marginal density for X and Y . (c). Compute Cov(X,Y ). Are X and Y independent?
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
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]
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...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT