X is a random variable with moments, E[X], E[X^2], E[X^3], and so forth. Prove this is true for i) X is discrete, ii) X is continuous
E[X-mu]^4 = E(X^4) - 4[E(X)][E(X^3)] + 6[E(X)]^2[E(X^2)] - 3[E(X)]^4
The Attempt at a Solution
I've been trying to generalize expanding the variance, E[(X-mu)^2], into the above result with no success. Not sure about the discrete and continuous proofs either. Anyone have any ideas?