Alvin likes to sail each Saturday to his cottage on a nearby island off the coast. Alvin is an avid fisherman, and enjoys fishing off his boat on the way to and from tha island, as long as the weather is good. Unfortunately, the weather is good on the way to or from the island with probability p, independent of what the weather was on any past trip ( so the weather would be nice on the way to the island, but poor on the way back). Now, if the weather is nice, Alvin will take one og his n fishing rods for the trip, but if the weather is bad, he will not bring a fihing rod with him. We want to find the probability that on a given leg of the trip to or from the island the weather will be nice, but Alvin will not fish because all his fishing are at his other home. (a) Formulate an appropriate Markov chain model with n + 1 states and find the steady-state probabilities. (b) What is the stead-state probability that on a given trip, Alvin sails with nice weather but without fishing rod.

Tuesday, January 30 th • Example 5: A positive correlation (r = 0.65) was found between ice tea consumption and the frequency of bee stings. Which of the following is the best explanation a. People who drink a lot of ice tea are more likely to be stung by bees than people who don’t. b. Drinking ice tea attracts bees and results in more bee sting cases. c. People drink more ice tea in the summer and bee stings are