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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 п. (п - 1) •. 2 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?

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 п. (п - 1) •. 2 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?

A First Course in Probability (10th Edition)
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...
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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 п. (п — 1) 2 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 п. (п — 1) 2 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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