1. On a busy day, the number of calls you receive in the day has a Poisson distribution with parameter 15, while on an ordinary day, the number of calls you receive in the is has a Poisson distribution with parameter 5. Suppose tomorrow will be a busy day with probability 0.6, and an ordinary day with probability 0.4. What is the probability that you receive 10 calls tomorrow?
2. 2. Fix an integer r 1. In a sequence of Bernoulli trials with probability of success p, let X be the number of games until the rth success.

(a)What values can X take? Find the probability mass function of X.

(b)Find E[X].

(c)Suppose Boston Celtics beats LA Lakers with probability .6 in each game, independent of their other games. Suppose they play in NBA playoffs, and the first team that wins four games wins the series. Use part (a) to find the probability that Boston Celtics wins the series in the sixth game. (Remark: compare your result with the result we obtained in class.)

3. Earthquakes are measured using Richter magnitude scale. Suppose when an earthquake occurs, the scale of the earthquake is a random variable that can be any positive number {1, 2, 3, 4, ...}, and the probability that the scale of the earthquake is k (k = 1, 2, 3, ..) is equal to c 0.1k, when c is a constant.

(a)Find c.

(b)Suppose the damage cost of an earthquake with scale k is 10k dollars. When an earth-quake occurs, what is the expected damage cost?

(c)Now suppose in real life, the scale of an earthquake can only be 1, 2, 3, ..., 9, 10. Repeat parts a and b.