Let Fx be the cumulative distribution function of the random

Let F(x) be the cumulative distribution function of the random variable X. If m is a number such that F(m)=1/2, show that m is a median of the distribution.

Solution

by definiton of cumulative distribution function, F(m) = P(X <= m)

definition of median is that: P(X <=m) = 0.5

Thus m is indeed median.