Thread: 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

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?

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?