# Math Help - pdf symmetric about a

1. ## pdf symmetric about a

If X is a continuous random variable symmetric about some point a, how do I show that E(X) = a? Thanks.

2. Break the integral into two parts.

$E(X)=\int_{-\infty}^axf(x)dx+\int_a^{\infty}xf(x)dx$

Let $x=a-u$ in the first integral and $x=a+u$ in the second.

Note that $f(a-u)=f(a+u)$