Multivariate Probability Distributions

**atalay** · April 28th 2010, 06:17 AM

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

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

Therefore, for finding c,

$\int_1^0$ $\int_x2^1$
is it rigt?

**mr fantastic** · April 28th 2010, 06:22 AM

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

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

Therefore, for finding c,

$\int_1^0$ $\int_x2^1$
is it rigt?

Draw the region defining the support. Then it is crystal clear that you require $\int_{x = -1}^{x = 1} \int_{y = x^2}^{y = 1} f(x, y) \, dy \, dx = 1$ .

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