Alice and Bob are playing a game where in each round, each of them rolls a fair die indepen-dently. If both roll the same number, then the game is repeated. Otherwise the player withthe larger number wins. LetXbe the number of rounds until the game is decided.(a) (10 points) Determine the probability mass function ofX.(b) (5 points ) ComputeE[X].(c) (5 points ) Compute Pr[ Alice win].(d) (5 points) Assume that you get paid 10USD for winning in the first round, 1USD forwinning in any other round, and nothing otherwise. Compute your expected winnings.

As voters exit the polls, you ask a representative random sample of voters if they voted for a proposition. if the true percentage of voters who vote for the proposition is 63%, what is the probability that, in your sample, exactly 5 do not voted for the proposition before 2 voted for the proposition? the probability is

X-10/4 when x = –18 a 7 b –2 c –7 d 2

Francisco's credit card has an apr of 28.98%, calculated on the previous monthly balance. his credit card record for the last 7 months is shown in the table below francisco is trying to figure out what this all means. answer the following questions: what is the total amount that francisco has paid in interest over the 7 months? what is the total amount that francisco has made in payments over the 7 months? how much of francisco's payments have gone to paying down the principal on his account? what is francisco's new balance at the end of month 8? what will francisco be charged for interest for month 8?