1. Select which are the following statements are examples of random variables vs discreet variables.

a) Number of sales made by a salesperson in a week. 0, 1, 2, 3, ...

b) The number of bids received in a bond offering. 0, 1, 2, 3, ....

c) Number of customers waiting to be served in a restaurant at a particular time. 0, 1, 2, 3

d) The length of time between arrivals in a hospital 0

e) The weight of food bought in a supermarket. 0

2. A panel of 10 experts is asked to do wine tasting and assign a rating of 0, 1, 2 or 3 to the wine. A score is then obtained by adding together the ratings of the 10 experts.

a) How many samples points are in this experiment?

b) How many values can this random variable assume?

3. A researcher showed that the number of consecutive years that must be sampled until a dry year (drought) is observed can be modeled using the formula p(x) = (0.7)x-1 (0.3)x where x= 1, 2, 3, ....

a) Find the probability that exactly 3 years must be sampled before a drought year occurs.

4. Suppose an insurance company sell a $10,000 one-year term insurance policy at an annual premium of $290. Actuarial tables show that the probability of death during the next year for a typical person purchased the insurance is 0.001.

a) How much money the insurance company makes per policy sold?

5) 5. Supposed you invest a fixed sum of money in 5 businesses. Assume you know that 70% of such businesses are successful, the outcome of businesses are independent of one another and the probability distribution for the number (x) of successful businesses out of 5 is listed below

X 0 1 2 3 4 5 P(x) 0.002 0.029 0.132 0.309 0.360 0.168