Question
Two numbers are selected at random (without replacement) from positive integers 2, 3, 4, 5, 6 and 7. Let X denote the larger of the two numbers obtained. Find the mean and variance of the probability distribution of X.
| $\text{x}_\text{i}$ | $\text{p}_\text{i}$ | $\text{x}_\text{i}\text{p}_\text{i}$ | $\text{x}_\text{i}^2\text{p}_\text{i}$ |
| $3$ | $\frac{2}{30}$ | $\frac{6}{30}$ | $\frac{18}{30}$ |
| $4$ | $\frac{4}{30}$ | $\frac{16}{30}$ | $\frac{64}{30}$ |
| $5$ | $\frac{6}{30}$ | $\frac{30}{30}$ | $\frac{150}{30}$ |
| $6$ | $\frac{8}{30}$ | $\frac{48}{30}$ | $\frac{288}{30}$ |
| $7$ | $\frac{10}{30}$ | $\frac{70}{30}$ | $\frac{490}{30}$ |
| $\sum\text{x}_\text{i}\text{p}_\text{i}=\frac{17}{3}$ | $\sum\text{x}_\text{i}\text{p}_\text{i}^2=\frac{101}{3}$ |
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