MATLAB Program Probabilities of Scatters Node Over A Square Region

Question

Assume the same set up as in Q1—100 nodes scattered over a 100 X 100 square grid. Use Poisson distribution to find the following. Do not use Binomial distribution.

I) What is the probability that a node located somewhere at the center of a square region has no links with the other 99 nodes when d=30. You can use the calculator or write a program to find this probability.

Meu  = n * nLink/(n-1*n-1)

II) What is the probability that the same node has exactly 1 link when d=30.

X = 1

III) What is the probability that the node has exactly 2 links when d=30. Since you are doing the same thing, writing a small program would help.

IV) Now, repeat the process for 3, 4, 5, 6, …. links. Essentially, what you obtain is the degree distribution.

Just use a for loop in the program.

V) What is the Expected degree of that node?

VI) Plot the degree distribution (No. of links in the x-axis and corresponding probabilities on the y-axis).

VII) Compare the plots you obtained for d=30 from the program (Q1) and from the analysis. The best would be to draw on top of each other. Make sure you have the same range for the x and y axes. Do they plots agree with each other? Why?

Summary

This question belongs to MATLAB software and discusses about application of MATLAB in mathematics to write a program that scatter nodes uniformly randomly over a square region and to find various probabilities of nodes

Answer is in MATLAB format