i have the following question:
A coin is flipped n times with the probability of $\frac35$ for heads. Each heads gets you 2 points and tails -3 points. Let $R$ be the total sum of points after n flips. Calculate the Expected value and the variance of $R$
My question is this: can i define $X$-"number of heads" and $N$-"number of tosses" and say that $R = 2X-3(N-X)$, and go on from there according to the formulas, assigning $N=n$ wherever required? Or do i have to define $Y$-"number of tails"? because the latter is difficult when i have to calculate $E(XY)$ which i have no clue how to.