Variance, standard deviation and linear variance of a discrete random variable
Let X be a signed change in a quantity
The distribution of \(X\) is given below
The probability mass function is given on its discrete domain
\[p(x)=\begin{cases}\frac{1}{8} & x=-6\\\frac{3}{4} & x=-2\\\frac{1}{8} & x=2\end{cases},\quad x\in\{-6, -2, 2\}\]
| \(x\) | \(\Pr(X=x)\) |
|---|---|
| \(-6\) | \(\frac{1}{8}\) |
| \(-2\) | \(\frac{3}{4}\) |
| \(2\) | \(\frac{1}{8}\) |
Use the table of squared-value products below. The symbol ? marks an entry to complete
| \(x\) | \(\Pr(X=x)\) | \(x^2\Pr(X=x)\) |
|---|---|---|
| \(-6\) | \(\frac{1}{8}\) | \(\frac{9}{2}\) |
| \(-2\) | \(\frac{3}{4}\) | ? |
| \(2\) | \(\frac{1}{8}\) | ? |
Find the variance of X. Give the exact value