Question
Two cards are selected at random from a box which contains five cards numbered 1, 1, 2, 2, and 3. Let X denote the sum and Y the maximum of the two numbers drawn. Find the probability distribution, mean and variance of X and Y.
| x: | 2 | 3 | 4 | 5 |
| P(x): | 0.1 | 0.4 | 0.3 | 0.2 |
| xi | pi | xipi | xi2pi |
| 2 | 0.1 | 0.1 | 0.4 |
| 3 | 0.4 | 1.2 | 3.6 |
| 4 | 0.3 | 1.2 | 4.8 |
| 5 | 0.2 | 1.0 | 5.0 |
| $\sum\text{xp}=3.6$ | $\sum\text{x}^2\text{p}=13.8$ |
| x: | 1 | 2 | 3 |
| p(x): | 0.1 | 0.5 | 0.4 |
| yi | pi | yipi | yi2pi |
| 1 | 0.1 | 0.1 | 0.1 |
| 2 | 0.5 | 1.0 | 2.0 |
| 3 | 0.4 | 1.2 | 3.6 |
|
| $\sum\text{xp}=2.3$ | $\sum\text{x}^2\text{p}=5.7$ |
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