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Question
Find the expected value, variance and standard deviation of random variable X whose probability mass function (p.m.f.) is given below:
| X = x | 1 | 2 | 3 |
| P(X) | `1/5` | `2/5` | `2/5` |
Solution
`E(X)=sumx_iP(x_i)`
= `1(1/5)+2(2/5)+3(2/5)`
= `(1+4+6)/5`
= `11/5`
= 2.2
`E(X^2)=sumx_i^2P(x_i)`
= `1^2(1/5)+2^2(2/5)+3^2(2/5)`
= `(1+8+18)/5`
= `27/5`
= 5.4
Var (X) = E(X2) - [E(X)]2
= 5.4 - (2.2)2
= 5.4 - 4.84
= 0.56
S.D. = `sqrt(Var (X))`
= `sqrt0.56`
= 0.7483
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