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.

          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.

Added by Monique G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert David Nguyen

05/17/2022

Step 1

This is found by integrating the joint density function over all possible values of Y. In this case, Y ranges from 0 to x. So we have: fX(x) = ∫ from 0 to x of f(x,y) dy = ∫ from 0 to x of 8xy dy = 8x * ∫ from 0 to x of y dy = 8x * [1/2 * Show more…

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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.