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Question
If r.v. X assumes values 1, 2, 3, ……. n with equal probabilities then E(X) = `("n" + 1)/(2)`
Options
True
False
Solution
This statement is True.
Explanation:
| X | 1 | 2 | 3 | .... | n |
| P(X) | `(1)/"n"` | `(1)/"n"` | `(1)/"n"` | `(1)/"n"` |
E(X) = `sumx_"i"*"P"(x_"i")`
= `1(1/"n") + 2(1/"n") + 3(1/"n") + .... + "n"(1/"n")`
= `(1)/"n" (1 + 2 + 3 + .... + "n")`
= `(1)/"n". ("n"("n" + 1))/(2)`
= `("n" + 1)/(2)`.
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