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प्रश्न
Find the expected value and variance of r.v. X whose p.m.f. is given below.
| X | 1 | 2 | 3 |
| P(X = x) | `1/5` | `2/5` | `2/5` |
उत्तर
E(X) = `sum_("i" = 1)^3 x_"i"* "P"(x_"i")`
= `1(1/5) + 2(2/5) + 3(2/5)`
= `(1 + 4 + 6)/5`
= `11/5`
E(x2) = `sum_("i" = 1)^3 x_"i"^2* "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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