I want to calculate the median of several variables. The detail is as follow: For example, a, b and c are all random number from uniform distribution in certain range (different between each other). Then, if D=abc, and I want to know what's the median value of D.
Any method to do this? Please let me know. Thanks very much.
For a continuous probability distribution on $\left[a,b\right]$, the median is a number $x\in\left[a,b\right]$ s.t. $$ \int_{a}^{x}f\left(x\right)dx=1/2. $$ That is, the probability of the random variable $X<x$ is equal to that of $X>x$. Plug in the product distribution and solve the above.