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Alvie Singer lives at 0 in the accompanying diagram and has four friends who live at A, 8, 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 8), with each of the three possibilities having probability 1/3. In this way, Alvie continues to visit friends until he returns home. B D (a) Let X- the number of times that Alvie visits a friend. Derive the pmf of X. O px)-(3)..를 for x-0, 1, 2, 3.. O DOX) = ()*- * - for x = 1, 2, 3, . O poO-(금) 글 for x-0, 1. 2. 3. . O po) - G) ** . for x =- 1, 2, 3 . (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? O pV)-(금)'.를 for y -0,1. 2. 3.. O ptv) - (GY*² for - 0, 1, 2, 3, .. O R0- (금).y- 2.3.4 O B0-(금)·를 for y- 2, 3, 4 (c) Suppose that female friends live at A and C and male friends at 8 and D. If z - the number of visits to female friends, what is the pmf of 27 O p(z) (금)..씀 -1, 2,3,. O p(2) - 1(주).. 2-1. 2, 3,. z-1 O plz) = 2- 2, 3, 4, . 2-1 O De) - ((승)·쯤 -2,3, 4, ..

Alvie Singer lives at 0 in the accompanying diagram and has four friends who live at A, 8, 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 8), with each of the three possibilities having probability 1/3. In this way, Alvie continues to visit friends until he returns home. B D (a) Let X- the number of times that Alvie visits a friend. Derive the pmf of X. O px)-(3)..를 for x-0, 1, 2, 3.. O DOX) = ()*- * - for x = 1, 2, 3, . O poO-(금) 글 for x-0, 1. 2. 3. . O po) - G) ** . for x =- 1, 2, 3 . (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? O pV)-(금)'.를 for y -0,1. 2. 3.. O ptv) - (GY*² for - 0, 1, 2, 3, .. O R0- (금).y- 2.3.4 O B0-(금)·를 for y- 2, 3, 4 (c) Suppose that female friends live at A and C and male friends at 8 and D. If z - the number of visits to female friends, what is the pmf of 27 O p(z) (금)..씀 -1, 2,3,. O p(2) - 1(주).. 2-1. 2, 3,. z-1 O plz) = 2- 2, 3, 4, . 2-1 O De) - ((승)·쯤 -2,3, 4, ..

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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 (a) Let X = the number of times that Alvie visits a friend. Derive the pmf of X. for x = 0, 1, 2, 3, ... for. = ) - (금)· for x %- 0, 1, 2, 3, . )-(중)-를for x-1, 2, 3, .. O p(x) = O p(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? O plvy) = (글)글 fory = 0, 1, 2, 3, .. - 2 O pUv)= (금).글 fory = 0, 1, 2, 3, .. O p(y) = - for y = 2, 3, 4, ... O py)- (플).를 for y - 2, 3, 4, .. (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? z = 0 O p(z) = z = 1, 2, 3, ... z = 0 O p(z) = lE z= 1, 2, 3, .. 1 z = 1 O p(z) = z = 2, 3, 4, ... z = 1 O p(z) = (공)·음 2-2, 3, 4,
Transcribed Image Text: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 (a) Let X = the number of times that Alvie visits a friend. Derive the pmf of X. for x = 0, 1, 2, 3, ... for. = ) - (금)· for x %- 0, 1, 2, 3, . )-(중)-를for x-1, 2, 3, .. O p(x) = O p(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? O plvy) = (글)글 fory = 0, 1, 2, 3, .. - 2 O pUv)= (금).글 fory = 0, 1, 2, 3, .. O p(y) = - for y = 2, 3, 4, ... O py)- (플).를 for y - 2, 3, 4, .. (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? z = 0 O p(z) = z = 1, 2, 3, ... z = 0 O p(z) = lE z= 1, 2, 3, .. 1 z = 1 O p(z) = z = 2, 3, 4, ... z = 1 O p(z) = (공)·음 2-2, 3, 4,
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