Suppose I roll two six-sided dice and offer to pay you $10 times the sum of the numbers showing. (e.g., if I roll a 4 and a 5, I will pay you $10 * (5+4) = $90). The probability chart for each roll is given:
A) What is the expected payoff to you?
B) What is the variance of the payoff to you?
C) What is the standard deviation of the payoff to you?
Now we are going to play the game 100 times in a row.
A) What is the expected total payment to you (the sum of the payments from all 100 games)?
B) What is the standard deviation of your total payout?