1. Two standard six sided dice - one red and one blue are thrown, and the maximum of the numbers on the top is recorded as the random variable X.

(a)Give the probability distribution of X.

(b)A gambling game is designed based on the throw of these dice. You win $500 if the maximum of the numbers on the top is less than or equal to 3, lose $100 if it is greater than 5, and there is no payoff otherwise. How much do you expect to win on an average?

2. A random variable X has mean 2 and variance 4. Another random variable is defined as Y = 2 3/2 X. Find the mean and variance of random variable X + Y.

3.An exclusive concert hall knows that 10 percent of the people making reservations for a concert will not show up. Consequently, their policy is to sell 57 tickets for the hall that can hold only 55 people. What is the probability that all the people who show up for a particular concert would get a seat?