In Game 1 the chance of winning 1 dollar is 12/25 and the chance of losing 1 dollar is 13/25. Let W1 be the total winnings after playing Game 1 100 times.
Let $X_i$ be the total winnings of a single game
Calculate $E(W1)$ and $V(W1)$
So E(W1) is easy to calculate but I'm suspicious about the solution given for V(W1)
The solutions gives the answer as $100V(X_i)$
Is that the right solution? I'm a bit suspicious of it and we have been warned that some of the solutions are wrong.
The variance of the sum of independent variables is equal to the sum of the variances. In this case you have 100 independent, identically distributed (commonly known as i.i.d.) random variables, so the variance of their sum is 100 times the variance of any single one of them. So in this case the given solution is correct.