Question

Find the expected value for the random variable of an unbiased die

Answer 1

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