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
\[f(x)=\frac{2\left(14-x\right)}{8^2},\quad 6\le x\le 14\]
\[f(x)=0\quad\text{outside the stated support}\]
The support is \(6\le x\le 14\)
Use the table below. A question mark marks a value to complete
| Moment | Integral | Value |
|---|---|---|
| \(E(X)\) | \(\int_{6}^{14} xf(x)\,dx\) | ? |
What is the value of E(X)? Give the exact value