Variance, standard deviation and linear variance of a discrete random variable
Let X be the difference between two recorded counts
The distribution of \(X\) is given below
The probability mass function is given on its discrete domain
\[p(x)=\begin{cases}\frac{1}{18} & x=7\\\frac{8}{9} & x=9\\\frac{1}{18} & x=11\end{cases},\quad x\in\{7, 9, 11\}\]
| \(x\) | \(\Pr(X=x)\) |
|---|---|
| \(7\) | \(\frac{1}{18}\) |
| \(9\) | \(\frac{8}{9}\) |
| \(11\) | \(\frac{1}{18}\) |
Use the table of squared-value products below. The symbol ? marks an entry to complete
| \(x\) | \(\Pr(X=x)\) | \(x^2\Pr(X=x)\) |
|---|---|---|
| \(7\) | \(\frac{1}{18}\) | ? |
| \(9\) | \(\frac{8}{9}\) | ? |
| \(11\) | \(\frac{1}{18}\) | \(\frac{121}{18}\) |
Determine Var(X) from the distribution. Give the exact value