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?
MATLAB: An Introduction with Applications
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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab477019-d2bb-4f6a-b4f7-fc581b395d0c%2F2dc2be42-2f14-47c9-8760-29d37d0c262a%2Fqs2x2oc_processed.png&w=3840&q=75)
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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