Address all parts of the question. Explain or justify each step. Write on only o

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Address all parts of the question. Explain or justify each step. Write on only one side of the paper. Assemble pages in order. Use this page as a cover sheet. A hiker starts at point 0 on the map shown below. She first chooses a path at random and follows it to points, B_1, B_2, or B_3. From that point she chooses a new path at random and follows it to one of the pomts A_1, A_2, A_3, A_4,. A_5 A_6, or A_7. Use the Law of Total Probability to calculate the probability that the hiker arrives at point A_4. Suppose the hiker arrives at point A_4, but it is not known which route she took. Use Bayes' Rule to calculate the probability that she passed through point B_2. Suppose the hiker arrives at point A_4, but it is not known which route she took. Use Bayes' Rule to calculate the probability that she passed through point B_2. Compare this with Part (b). Let X denote the amount in pounds of polyurethane cushioning found in a car. The pdf for X is elsewhere Derive the mean, variance and standard deviation for X.

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