For a random variable X, show that Var(X) = E(X(X-1)) - E(X) ((E(X)-1)?

Question

There isn't anything else to add really. Any help would be GREATLY appreciated :)

Answer 1

You made at least one typo, obviously, since the parentheses don't line up.

That said, if I had the correct question in front of me and were looking for a proof -- well, what's the definition of variance??

Fiddle around with polynomials and use the fact that the expectation of the sum is the sum of the expectations, and similarly for difference and multiplication by a constant factor.

Just be careful not to make the false assumption that the expectation of the product is the product of the expectations.

Answer 2

The answer is 7x.