Mean, variance and standard deviation of a continuous random variable
Let X be the length, in centimetres, of a measured object
The probability density function of \(X\) is
\[f(x)=\frac{2\left(15-x\right)}{4^2},\quad 11\le x\le 15\]
\[f(x)=0\quad\text{outside the stated support}\]
The support is \(11\le x\le 15\)
Use the table below. A question mark marks a value to complete
| Moment | Integral | Value |
|---|---|---|
| \(E(X)\) | \(\int_{11}^{15} xf(x)\,dx\) | ? |
Determine E(X) from the density. Give the exact value