Question

Let X and Y be two random variables with joint density function f_{X,Y}(x, y) = { 2, 0 < x < y < 1, 0, o.w. } Find the marginal density function of the random variable X and find the marginal density function of the random variable Y

          Let X and Y be two random variables with joint density function
f_{X,Y}(x, y) = {
2, 0 < x < y < 1,
0, o.w.
}
Find the marginal density function of the random variable X and find the marginal density function of the random variable Y

Let X and Y be two random variables with joint density function
fX,Y(x, y) =
2, 0 < x < y < 1,
0, o.w.

Find the marginal density function of the random variable X and find the marginal density function of the random variable Y

Added by Nicholas B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

07/04/2023

Step 1

To do this, we need to integrate the joint density function with respect to the other variable. For the marginal density function of X, we integrate with respect to Y: $$f_X(x) = \int_{-\infty}^{\infty} f_{X,Y}(x,y) dy$$ Since the joint density function is only Show more…

Show all steps

Thanks for your feedback!

Let X and Y be two random variables with joint density function f(x,y) = Find the marginal density function of the random variable X and find the marginal density function of the random variable Y.