(adsbygoogle = window.adsbygoogle || []).push({}); Assume that two random variables (X,Y) are uniformly distributed on a circle with radius a. Then the joint probability density function is

[tex]f(x,y) = \frac{1}{\pi a^2}, x^2 + y^2 <= a^2[/tex]

[tex]f(x,y) = 0, otherwise[/tex]

Find the expected value of X.

E(X) = [tex]\int^{\infty}_{- \infty}\int^{\infty}_{- \infty}\frac{x}{\pi a^2} dxdy[/tex]

Is this correct so far? What are the limits of the integral supposed to be?

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# Homework Help: Expected value and joint probability density function

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