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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 1/3. 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 of visits to female friends, what is the pmf of*Z*?

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# Chapter 3 Solutions

Probability and Statistics for Engineering and the Sciences

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