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Question
The probability distribution of a discrete random variable X is given as under:
| X | 1 | 2 | 4 | 2A | 3A | 5A |
| P(X) | `1/2` | `1/5` | `3/25` | `1/10` | `1/25` | `1/25` |
Calculate: Variance of X
Solution
Now the distribution becomes
| X | 1 | 2 | 4 | 6 | 9 | 15 |
| P(X) | `1/2` | `1/5` | `3/25` | `1/10` | `1/25` | `1/25` |
E(X2) = `1 xx 1/2 + 4 xx 1/5 + 16 xx 3/25 + 36 xx 1/10 + 81 xx 1/25 + 225 xx 1/25`
= `1/2 + 4/5 + 48/25 + 36/10 + 81/25 + 225/25`
= 0.5 + 0.8 + 1.92 + 3.6 + 3.24 + 9.00
= 19.06
Variance (X) = E(X2) – [E(X)]2
= 19.06 – (2.94)2
= 19.06 – 8.64
= 10.42
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