5. A group of n people stand in a line. On the count of three, each of them simultaneously chooses to look either left or right (with equal probability): at one of their neighbors. Let X be the number of pairs of adjacent people that end up facing each other. (For example, if n = 5 and the random facings are "Left, Left, Right, Left, Right" then only the 3rd and 4th people face each other.) (a) Find the expected value E[X]. (b) Find Pr[X=0]. (c) Assuming n is even, find the maximum possible value of X, and the probability that X is equal to that value.
5. A group of n people stand in a line. On the count of three, each of them simultaneously chooses to look either left or right (with equal probability): at one of their neighbors. Let X be the number of pairs of adjacent people that end up facing each other. (For example, if n = 5 and the random facings are "Left, Left, Right, Left, Right" then only the 3rd and 4th people face each other.) (a) Find the expected value E[X]. (b) Find Pr[X=0]. (c) Assuming n is even, find the maximum possible value of X, and the probability that X is equal to that value.
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...
Related questions
Question
![5. A group of n people stand in a line. On the count of three, each of them simultaneously
chooses to look either left or right (with equal probability): at one of their neighbors.
Let X be the number of pairs of adjacent people that end up facing each other. (For example,
if n = 5 and the random facings are "Left, Left, Right, Left, Right" then only the 3rd and 4th
people face each other.)
(a) Find the expected value E[X].
(b) Find Pr[X=0].
(c) Assuming n is even, find the maximum possible value of X, and the probability that X
is equal to that value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F232028c3-8426-43ce-b04a-a507a5240356%2Ffbce8656-b213-4d23-817e-d6775ccaaf6f%2F37keyvv.jpeg&w=3840&q=75)
Transcribed Image Text:5. A group of n people stand in a line. On the count of three, each of them simultaneously
chooses to look either left or right (with equal probability): at one of their neighbors.
Let X be the number of pairs of adjacent people that end up facing each other. (For example,
if n = 5 and the random facings are "Left, Left, Right, Left, Right" then only the 3rd and 4th
people face each other.)
(a) Find the expected value E[X].
(b) Find Pr[X=0].
(c) Assuming n is even, find the maximum possible value of X, and the probability that X
is equal to that value.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps

Recommended textbooks for you

A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON


A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
