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The value of C for which joint probability density function of random variables x and y as
fXY(x, y) = C (1 – x – y)
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- 2
- 4
- 6
- 8
Correct Option: C
| FXY(x, y) = |  | ∞ | | ∞ | C(1 – x – y)dx dy = 1 | –∞ | –∞ |
| 1 = | | 1 | | 1-x | C(1 – x – y)dx dy | 0 | 0 |
 |
| 1 = | | 1 | C |  | (1 – x).y – |  | 1-x | dx | 0 | 2 | 0 |
| 1 = C | | 1 | | (1 – x)(1 – x) – | | dx | 0 | 2 |
| 1 = C | | 1 | dx | 0 | 2 |
| 1 = | | x + | - 2 | | 1 | 2 | 3 | 2 | 0 |
| 1 = | | 1 + | - 1 | | 2 | 3 |
or C = 6
