On page 18-21 of your textbook, the authors show that the binominal distribution

Question

On page 18-21 of your textbook, the authors show that the binominal distribution takes on a Gaussian shape for large N You will us Mathematics program to simulate the bi-normal distribution by generation random coin flips. Mathematics is available on the computers in the microlabs. With Mathematica running, just type in commands. Mathematica executes the commands when you hit SHIFT -ENTER. If you make a mistake you can go back to the command edit it or re-type it, then hit SHIFT-Enter again. Mathmatica will the old result and exe4cute the revised command. Use the HELP menu if you need to To get started, here is way to , find the number of, repent the whole trial N times and them histogram the result. In the example below m = 10 and N = 200; Notice the when you define a function the variable name on the hand side of the definition is followed by the underscore, hence instead of m. Have Mathematica repeat the m = 400 coin toes experiment N = 400, 4000 and 40000 times. The resulting histograms should gradually become pretty smooth. Give names to the histograms, such as P1 = Histogram so you can show can is again later Now graph histogram. Note that the normalized Gaussian function G(r) = and see how well it matches your histogram. Note that the normalized Gaussian must be multiplied by the number of trials N to much the histogram. I Suggest to x-axis limits of 160 to 240, since the function is at m/2 = 200. Use command show [p1, G] to plot your result together.

Explanation / Answer

When I did this for class I used his example for mathematica and changed m and N in the equations. But you have to remember to shift + enter to make changes. N is times of experiment and m I believe would be heads. For Historgram[ManyTrials[200]] N would be the 200 and the 10 in second line would be m. Don't know how to graph the Gaussian function so if you rate needs work it would be understandable.

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