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Andy, Bob, and Charley have all been serving time for grand theft auto. According to prison scuttlebutt, the warden plans to release two of the three next week. They all have identical records, so the two to be released will be chosen at random, meaning that each has a two-thirds probability of being included in the two to be set free. Andy, however, is friends with a guard who will know ahead of time which two will leave. He offers to tell Andy the name of one prisoner other than himself who will be released. Andy, however, declines the offer, believing that if the learns the name of one prisoner scheduled to be released, then his chances of being the other person set free will drop to one-half (since only two prisoners will be left at that point). Is his concern justified?
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An Introduction to Mathematical Statistics and Its Applications (6th Edition)
- The weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 40% chance it will be good tomorrow, a 30% chance it will be indifferent, and a 30% chance it will be bad. If the weather is indifferent today, there is a 50% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be good tomorrow and a 30% chance it will be indifferent. The stochastic matrix for this situation is shown to the right. In the long run, how likely is it for the weather in Columbus to be indifferent on a given day? P= 0.4 0.5 0.1 0.3 0.2 0.3 0.3 0.3 0.6 In the long run, how likely is it for the weather in Columbus to be indifferent on a given day? % (Round to the nearest integer as needed.)arrow_forwardThe weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 40% chance it will be good tomorrow, a 30% chance it will be indifferent, and a 30% chance it will be bad. If the weather is indifferent today, there is a 50% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be good tomorrow and a 30% chance it will be indifferent. a. What is the stochastic matrix, P, for this situation? b. Suppose there is a 10% chance of good weather today and a 90% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 40% indifferent weather and 60% bad weather. What are the chances for good weather on Wednesday? a. Create the stochastic matrix, P, where G is good, I is indifferent, and B is Bad. From: GIB a (Simplify your answers.) To: Garrow_forwardThe weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 40% chance it will be good tomorrow, a 40% chance it will be indifferent, and a 20% chance it will be bad. If the weather is indifferent today, there is a 60% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be good tomorrow and a 30% chance it will be indifferent. a. What is the stochastic matrix, P, for this situation? b. Suppose there is a 40% chance of good weather today and a 60% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 90% indifferent weather and 10% bad weather. What are the chances for good weather on Wednesday? a. Create the stochastic matrix, P, where G is good, I is indifferent, and B is Bad. From: a P G B (Simplify your answers.) To: G I Barrow_forward
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