Address all parts of the question Explain or justify each st

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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