Chapter 12.3, Problem 19E

If $X$ is a random variable with density function $f\left(x\right)$ on $A\le x\le \text{}B$, the median of $X$ is that number $M$ such that ${\displaystyle {\int }_0^{M}f\left(x\right)dx=\frac{1}{2}}$.

In other words, $\mathrm{Pr}\left(X\le M\right)=\frac{1}{2}$.

Find the median of the random variable whose density function is $f\left(x\right)=\frac{1}{18}x,0\le x\le 6$.