Median, quartiles and percentiles of a continuous random variable
Let X be the rainfall, in millimetres, recorded in one event
The density of X is given on its support below
\[f(x)=-\frac{1}{6}x+\frac{37}{12},\quad 15\le x\le 18\]
\[f(x)=0\quad\text{outside the stated support}\]
The support is \(15\le x\le 18\)
The required cumulative probability is \(\frac{1}{2}\)
What is the median value for X? Give the exact value