In this question we explore the application of maximum likelihood estimation in a social network. Suppose we have n people in a social network, labeled as Q1,..., Qn. Each person may or may not know another person; we denote this relationship as Xij, where (assuming i #j) [1 if (i, j) are acquaintances Xij |0 otherwise. We further assume that the "friendliness" of these people are the same, i.e., Xij Ber(p) in all cases where i + j. Our goal is to use maximum likelihood to estimate p. We approach this by surveying each person and ask how many friends he/she has (not counting friend with himself/herself, of course). Suppose n = 5, and our responses are: Q1:2 friends Q2 :4 friends Q3 :3 friends Q4 :2 friends Q5 :3 friends What is the ML estimate of p?

In this question we explore the application of maximum likelihood estimation in a social network. Suppose we have n people in a social network, labeled as Q1,..., Qn. Each person may or may not know another person; we denote this relationship as Xij, where (assuming i #j) [1 if (i, j) are acquaintances Xij |0 otherwise. We further assume that the "friendliness" of these people are the same, i.e., Xij Ber(p) in all cases where i + j. Our goal is to use maximum likelihood to estimate p. We approach this by surveying each person and ask how many friends he/she has (not counting friend with himself/herself, of course). Suppose n = 5, and our responses are: Q1:2 friends Q2 :4 friends Q3 :3 friends Q4 :2 friends Q5 :3 friends What is the ML estimate of p?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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