MATH 367, spg 98 PROJECT 3: Poisson Approximation Due: Wed Apr 1

NAME:

You need an account in the VAX cluster to do this project. We will use the statistical program MINITAB. Just type MINITAB at the prompt. (If this doesn’t work, type prepare minitab, hit return, and then type minitab).

To be able to write what you do onto a file that you can later edit, type MTB > outfile ‘project3’ This will create a file called: project3.lis;1.

MINITAB stores data into “columns” called: C1,C2,…, etc. Constants are stored into K1, K2, … etc.

In the following, we are going to set an array C1 with the counters from 0 to 50: MTB > set c1 DATA> 0:50 DATA> end Now, we are going to put the probabilities of a Binomial n = 50 and p = 1/2 into the array C2, that is, the entries of C2 are P (X = k) from k = 0, …, 50: MTB > pdf c1, put into c2; SUBC> binomial 50, .5. Now we do the same for the Poisson with mean 50(1/2) = 25: MTB > pdf c1, put into c3; SUBC> poisson 25. Now we plot both together: MTB > mplot c2 vs c1 c3 vs c1 Or you could compare the difference of the probabilities by looking at the absolute value of their differences: MTB > let c4=absolute(C2-C3) MTB > print c4

If you want to look at the plot where the values are more relevant, you can do the following: MTB > set c4 DATA> 12:40 DATA> end MTB > pdf c4, put into c5; SUBC> binomial 50, .5. MTB > pdf c4, put into c6; SUBC> poisson 25. MTB > mplot c5 vs c4 c6 vs c4 In C5 and C6 we have the probability values for k = 12, …, 40 of a binomial(50,1/2) and a Poisson with mean 25. Problem: Use this method to compare (a) a Binomial (50,.2) against the corresponding Poisson, (b) a Binomial (100,.1) against the appropriate Poisson. That is , you will plot the binomial and Poisson together as I did in the example, and look at the absolute values of their differences. (c) By looking at the absolute value of their differences, compute what the error of estimation is.