[Math] the expected product of heads and tails if a coin flipped 10 times

Question

What is the expected value of the product of heads and tails of a fair coin flipped 10 times?

What is the expected product if the coins are biased? P(H)=1/3 P(T)=2/3? 10 flips.

Answer 1

We still have $$E[X(n-X)]=E[nX-X^2]=E[nX]-E[X^2]=nE[X]-V[X]-E[X]^2$$ Just supply the values of $E[X]=np$ and $V[X]=npq$