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Variance of X if
fx(x) = 
3(1 – x)2; for 0 ≤ x ≤ 1 0; otherwise
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3 80 -
1 30 -
2 50 -
1 6
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Correct Option: A
Variance, σ2 x = E[x2] – (μx)2
| E[x2] = 3 |  | 1 | x2 (1 – x)2dx | a |
| = 3 | | 1 | (x2 – 2x3 + x4)dx | a |
| E[x2] = 3 |  | - | + |  | 1 | 3 | 4 | 5 | 0 |
| = 3 | | - | + | | 3 | 2 | 5 |
| = 3 | | | 30 |
= 3 × 1/30
= 1/10
Now,
σ2x = 1/10 – (1/4)2
| = | – | = | 10 | 16 | 160 |
= 6/160
= 3/80
