Expectation of a Variable

Quote:

dice has faces numbered 1 to 6 and is weighted so that the probability of

throwing n (n = 1; 2; :::; 6) in a single throw is proportional to n, i.e., equals

Cn for some constant C.

(a) Find C .

(b) Let X be equal to the number shown when the dice is thrown.

i) Compute E(X^3).

I've calculated C as 1/21.

However, i thought the expectation of E(x^3) would thus be:

E(X^3) = n^3/21

so: 1/21 + 2^3/21 + 3^3/21 etc....

EDIT: Is Latex now working? I keep getting errors whilst using it.

Thankyou :)