distribution of a continuous random variable X is symmetric

The distribution of a continuous random variable X is symmetric about the value c if the pdf f(x) of X is such that f(c − x) = f(c + x) for all real numbers x.

(a) Show that if X is symmetric about 0, both the mean and the median of X are 0.

Any help would be greatly appreciated :)

Re: distribution of a continuous random variable X is symmetric

Do you know what the mean and median **are**? If you were given the distribution function, f, how would you find the mean? How would you find the median?

Re: distribution of a continuous random variable X is symmetric

Well, the median is F(x)=0.5, for the cdf, and the mean could be found by finding the mgf and the first moment about 0, or by finding the integral of xf(x) with limits infinity and -infinity. How would this information help in the proof?