Question

3) The joint probability density function of X and Y is given by f(x,y) = c(y^2 - 2x^2) e^-y -y ? x ? y, 0 < y < ? a) Find c. b) Find the marginal densities of X and Y.

          3) The joint probability density function of X and Y is given by
f(x,y) = c(y^2 - 2x^2) e^-y -y ? x ? y, 0 < y < ?
a) Find c.
b) Find the marginal densities of X and Y.

Added by Leslie A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

07/18/2023

Step 1

To do this, we need to integrate the joint probability density function over the entire range of x and y, and set the result equal to 1. $$ 1 = \int_{0}^{\infty} \int_{x}^{\infty} c(y^2 - 2x^2)e^{-y} dy dx $$ Now, let's solve the inner integral Show more…

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The joint probability density function of X and Y is given by f(x,y) = c(y^2 - 2x^2) e^-y -y ≤ x ≤ y, 0 < y < ∞ a) Find c. b) Find the marginal densities of X and Y.