Median, quartiles and percentiles of a continuous random variable
Let X be the response time, in seconds, of a device
Consider the continuous random variable X described by this density
\[f(x)=-\frac{1}{24}x+\frac{7}{24},\quad 0\le x\le 6\]
\[f(x)=0\quad\text{outside the stated support}\]
The support is \(0\le x\le 6\)
The required cumulative probability is \(\frac{1}{2}\)
Determine the value of the median. Give the exact value