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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 | 0 | 1 |
| 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) + 0(2/5) + 1(2/5)`
= `(1)/(5)`
E(X2) = \[\sum\limits_{i=1}^{3} x_i^2\text{P}(x_i)\]
= `(-1)^2 (1/5) + 0^2(2/5) + 1^2(2/5)`
= `(3)/(5)`
∴ Var(X) = E(X2) – [E(X)]2
= `(3)/(5) - (1/5)^2`
= `(14)/(25)`..
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