Monday

Homework Read section 9.1 and 9.2. From section 9.1 do numbers 1,3,4,10,12 and resolve the sign error from the computation in class. The hint is that the place we thought the sign error was likely was in fact evaluated correctly! Look at the other terms closely.

We will meet for x-session tomorrow and hopefully get back and go over the exam.

Comments stats[statevalf,cdf,normald](.56);

stats[statevalf,pdf,normald](.56);

Here is are the programs explored on Monday.

Dsum := proc(n,p) local i,new,U,X,Y; U := NFoldConvolution([[0,1-p],[1,p]],n); new := []; for i from 1 to n do new := [op(new), [evalf(U[i][1] ),evalf((1)*(U[i][2]))]]; od; new; Spikegraph(new, 0, n ,true ); end:

Dsum(40,1/9);

DCentral := proc(n,p) local i,new,U,X,Y; U := NFoldConvolution([[0,1-p],[1,p]],n); new := []; for i from 1 to n do new := [op(new), [evalf(((U[i][1] - n*(p))/sqrt((p*(1-p))*n)) ), evalf(sqrt((p*(1-p))*n)*(U[i][2]))]]; od; new; X := Spikegraph(new, -6,6,true ); Y := plot((1/(sqrt(2*Pi)))*exp(-x^2/2),x = -6 .. 6); display(X,Y);end:

DCentral(40,1/9);

Bsum := proc(n,p) local i,new,U,X,Y; U := NFoldConvolution([[1,p],[0,0],[-1,p]],n); new := []; for i from 1 to 3*n - n do new := [op(new), [evalf(U[i][1] ),evalf((1/2)*(U[i][2]))]]; od; new; Spikegraph(new, -n, n ,true ); end: Bsum(20,1/9);

BCentral := proc(n,p) local i,new,U,X,Y; U := NFoldConvolution([[1,p],[0,0],[-1,1-p]],n); new := []; for i from 1 to 3*n - n do new := [op(new), [evalf(((U[i][1] - n*(2*p-1))/sqrt((1-(2*p-1)^2)*n)) ), evalf((1/2)*sqrt((1-(2*p-1)^2)*n)*(U[i][2]))]]; od; new; X := Spikegraph(new, -6,6,true ); Y := plot((1/(sqrt(2*Pi)))*exp(-x^2/2),x = -6 .. 6); display(X,Y);end: BCentral(40,1/9);

Wednesday

Homework

Read 9.2 and 9.3. Do problems 1,2,5,6,10,11 and 15 from 9.2.

Comments:

Here is the maple code played with in todays lecture.

f := n-> stats[statevalf,cdf,normald](evalf((-n)/sqrt(n))) + stats[statevalf,cdf,normald](evalf((1500-n)/sqrt(n)));

Friday

Homework Read 9.3 and 10.3. From 9.3 do 3,4,7,10 and 14 and from section 10.3 do 1 and 2. Notice that the program required for problem 9.3 7 is mearly a slight modification away from a program in our week 7 weekly log and is not meant to be difficult (with that said dealing with parts d and e may require a bit of thinking).

Comments I think the most profitable way to end this class is to explore the random walks we played with in the first week of class. So our schedule will be

1.

10.3 - giving us a deeper understand of the central limit theorem.

2.

12.1 (and 10.1) random walks and wondering around.

3.

Then where do we go from here. A breaif look into the facinating world of Brownian motion (where random walk meet the central limit theorem).