Continuous random median

Remember that the median of any distribution is the value in the middle: 50% of the data is below it and 50% of the data is above it.

When talking about probability and distributions, the median is where the probability is 0.5.

Finding a formula

Knowing our formula for finding the probability of a continuous random variable, P(a \leq X \leq b) = \int_a^b f(x)\,dx, as well as that the median is where the probability is 0.5, we can find that:

\int_0^mf(x)\,\,dx=0.5

We can use definite integration and find the value of m - that’s the median.