Question
Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).
| $\text{x}_i$ | $\text{f}_i$ | $\text{p}_i$ | $\text{p}_i\text{x}_i$ |
| $2$ $3$ $4$ $5$ $6$ |
$2$ $4$ $6$ $8$ $10$ |
$\frac{2}{30}$ $\frac{4}{30}$ $\frac{6}{30}$ $\frac{8}{30}$ $\frac{10}{30}$ |
$\frac{4}{30}$ $\frac{12}{30}$ $\frac{24}{30}$ $\frac{40}{30}$ $\frac{60}{30}$ |
| $30$ | $\sum\text{p}_i\text{x}_i=\frac{140}{30}$ |
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