3 points DevoreStat93. E.026. My Notes Ask Your Teacher Alvie Singer lives at 0

Question

3 points DevoreStat93. E.026. My Notes Ask Your Teacher 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 p(x)-(·for x-0,1,2,3, p(x)-(·for x-o, 1, 2, 3, o(x) _ (-1 p(x)-(1 for x = 1, 2, 3, for x = 1, 2, 3, (b) Let Y = the number of straight-line segments that Alvie traverses (including those leading to and from op. what is the pmf of Y? p(y) _ (3),-2 for -o, 1, 2, 3 oly)-()for y-o, i, 2, 3, an-(4),-2.for y _ 2, 3, 4 p(y) _ (3), for y = 2, 3, 4, … ·

Explanation / Answer

from above

a) p(x) =(2/3)x-1*(1/3) for x =1,2,3,....

b)

p(y)=(2/3)y-2*(1/3) for y=2 ,3,4,...

c)

1/6 z=0 p(z)= (4/9)z-1*(25/54) z=1,2,3,4,…

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