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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
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Alvie Singer lives at 0 in the accompanying diagram and

Chapter 4, Problem 26E

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QUESTION:

Alvie Singer lives at 0 in the accompanying diagram and has four friends who live at A, B, C, and D. One day Alvie decides to go visiting, so he tosses a fair coin twice to decide which of the four to visit. Once at a friend’s house, he will either return home or else proceed to one of the two adjacent houses (such as 0, A, or C when at B), with each of the three possibilities having probability . In this way, Alvie continues to visit friends until he returns home. a. Let X = the number of times that Alvie visits a friend. Derive the pmf of X. b. ?Let Y= the number of straight-line segments that Alvie traverses (including those leading to and from 0). What is the pmf of Y? c. ?Suppose that female friends live at A and C and male friends at B and D. If Z = the number f visits to female friends, what is the pmf of Z?

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QUESTION:

Alvie Singer lives at 0 in the accompanying diagram and has four friends who live at A, B, C, and D. One day Alvie decides to go visiting, so he tosses a fair coin twice to decide which of the four to visit. Once at a friend’s house, he will either return home or else proceed to one of the two adjacent houses (such as 0, A, or C when at B), with each of the three possibilities having probability . In this way, Alvie continues to visit friends until he returns home. a. Let X = the number of times that Alvie visits a friend. Derive the pmf of X. b. ?Let Y= the number of straight-line segments that Alvie traverses (including those leading to and from 0). What is the pmf of Y? c. ?Suppose that female friends live at A and C and male friends at B and D. If Z = the number f visits to female friends, what is the pmf of Z?

ANSWER:

Answer: Step 1 of 1 Alvie Singer lives at 0 in the accompanying diagram and has four friends who live at A, B, C, and D. One day Alvie decides to go visiting, so he tosses a fair coin twice to decide which of the four to visit. Once at a friend’s house, he will either return home or else proceed to one of the two adjacent houses (such as 0, A, or C when at B), with each of the three possibilities having probability. a) Alvie visits 1 friend = (1/3) Alvie visits 2 friends = (2/3)(1/3) A

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