Each day, mice are put into a T maze. In this maze they have a choice of turning left (are rewarded with cheese) or to the right (receive cheese along with mild shock). After the first day, their decision whether to turn right or left is influenced by what happened on the previous day. Of those that go to the left on a certain day, 90% go to the left and the next day 10% go to the right. Of those that go to the right on a certain day, 60% go to the left on the next day and 30% go to the right. a. Set up a stochastic matrix with columns and rows labeled L and R that describes this situation b. Compute the second power of martrix in part a c. Suppose that the first day (day 0), 50% go to the left and 50% go to the right. So the initial distribution is given by the column matrix .5 and .5 using the matrixes in part a and part b find the distribution matrixes for the next two days , day 1 and day 2 d. Make a guess as to the percentage of mice that will go to th left after 50 days.
Each day, mice are put into a T maze. In this maze they have a choice of turning left (are rewarded with cheese) or to the right (receive cheese along with mild shock). After the first day, their decision whether to turn right or left is influenced by what happened on the previous day. Of those that go to the left on a certain day, 90% go to the left and the next day 10% go to the right. Of those that go to the right on a certain day, 60% go to the left on the next day and 30% go to the right.
a. Set up a stochastic matrix with columns and rows labeled L and R that describes this situation
b. Compute the second power of martrix in part a
c. Suppose that the first day (day 0), 50% go to the left and 50% go to the right. So the initial distribution is given by the column matrix .5 and .5 using the matrixes in part a and part b find the distribution matrixes for the next two days , day 1 and day 2
d. Make a guess as to the percentage of mice that will go to th left after 50 days.
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