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Question
Find the expected value for the random variable of an unbiased die
Solution
When a un based die is thrown, any one of the number 1, 2, 3, 4, 5, 6, can turn up that x denote the random variable taking the values from 1 to 6
| x | 1 | 2 | 3 | 4 | 5 | 6 |
| P(X = x) | `1/6` | `1/6` | `1/6` | `1/6` | `1/6` | `1/6` |
Expected values of the number on a die
= `"E"(x)`
= `sum_("i" = 1)^"n" "P"_("i'x"i")` = 1
= `(1/6 xx 1) + (1/6 xx 2) + (1/6 xx 3) + (1/6 xx 4) + (1/6 xx 5) + (1/6 xx 6)`
`1/6 [1 + 2 + 3 + 4 + 5 = 6]`
= `21/6`
= `7/2`
= (3.5)
∴ E(x) = 3.5
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