1. ## Multivariate Probability Distributions

If the random variables X and Y have the joint pdf:

f (x, y)= { cx^2y for x^2<=y<=1
0, elsewhere

Find c?
i know

$\displaystyle \int_a^b$ $\displaystyle \int_c^d$ f(x, y) dxdy=1 for a<y<b, c<x<d.

Therefore, for finding c,

$\displaystyle \int_1^0$$\displaystyle \int_x2^1 is it rigt? 2. Originally Posted by atalay If the random variables X and Y have the joint pdf: f (x, y)= { cx^2y for x^2<=y<=1 0, elsewhere Find c? i know \displaystyle \int_a^b \displaystyle \int_c^d f(x, y) dxdy=1 for a<y<b, c<x<d. Therefore, for finding c, \displaystyle \int_1^0$$\displaystyle \int_x2^1$
is it rigt?
Draw the region defining the support. Then it is crystal clear that you require $\displaystyle \int_{x = -1}^{x = 1} \int_{y = x^2}^{y = 1} f(x, y) \, dy \, dx = 1$.