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Question
Solve the following problem :
Find the expected value and variance of the r. v. X if its probability distribution is as follows.
| x | 1 | 2 | 3 |
| P(X = x) | `(1)/(5)` | `(2)/(5)` | `(2)/(5)` |
Solution
E(X) = \[\sum\limits_{i=1}^{3} x_i\cdot\text{P}(x_i)\]
= `1(1/5) + 2(2/5) + 3(2/5)`
= `(1 + 4 + 6)/(5)`
= `(11)/(5)`
E(X2) = \[\sum\limits_{i=1}^{3} x_i^2\cdot\text{P}(x_i)\]
= `1^2(1/5) + 2^2(2/5) + 3^2(2/5)`
= `(1 + 8 + 18)/(5)`
= `(27)/(5)`
∴ Var(X) = E(X2) – [E(X)]2
= `(27)/(5) - (11/5)^2`
= `(14)/(25)`.
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