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?

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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
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?
Transcribed Image Text: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 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?
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