If we observe a random realization of this graph model to have m edges, then what is the maximum likelihood estimate for p in terms of n and m? n-1 n - 1

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Suppose we have an Erdos-Renyi model G (n, p). Let m be the number of edges of the graph.
What is the expected number of edges in terms of n and p?
(For the problems in this course, if you arrive at any expressions in terms of binomial coefficients such as \binom {b,k}\, enter
a simplified algebraic expression without binomial coefficients. )
E [m] =
((n*(n-1))/2)*p
(-):
n: (n -
If we observe a random realization of this graph model to have m edges, then what is the maximum likelihood estimate for p
in terms of n and m?
=
n-1
п — 1
Transcribed Image Text:Suppose we have an Erdos-Renyi model G (n, p). Let m be the number of edges of the graph. What is the expected number of edges in terms of n and p? (For the problems in this course, if you arrive at any expressions in terms of binomial coefficients such as \binom {b,k}\, enter a simplified algebraic expression without binomial coefficients. ) E [m] = ((n*(n-1))/2)*p (-): n: (n - If we observe a random realization of this graph model to have m edges, then what is the maximum likelihood estimate for p in terms of n and m? = n-1 п — 1
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