"Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, are are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity." -- (Mary Somerville, 1780-1972) David Hume (Scotland, 1711-1776): One of a number of eighteenth-century philosophers who did not believe in the doctrine of an external world following fixed mathematical laws. As did Immanuel Kant (1724-1804), Hume claimed that mathematics is not inherent in the physical world but comes from the human mind. The intuitionist school of mathematical thought that was founded by Dutch mathematician Luitzen Brouwer (1881-1966) built their beliefs around the philosophies of Hume and Kant. What did Herkimer do when the police where chasing him for stealing a set of bathroom scales? Answer: He stopped and stepped on the scales so he could get a weigh. Herky's friends: ALLISON WONDERLAND...she loved the stories written by Lewis Carroll. EDDIE TORIAL...this guy wrote a daily newspaper column. ASSIGNMENT #52 Reading: Review, as necessary. Exercises: Handouts (multiple choice exercises) distributed in class. Do Set 1a (Interpreting Graphical Displays) and Set 1b (Summarizing Distributions with Numerical Data) NOTE: No new material will be covered during this first semester. We will begin the second semester with Assignment #53 which will take us into Chapter 9. Assignments for the next two days will consist of review sheets handout out in class. You are working with ideas and concepts fromChapter 8.

Example of geometricdistribution: Roll a die, and let x bethen number of rolls until the first 6 is obtained. Then x is amember of the infinite set {1,2,3,4,......}. Here are probabilitiesfor some values of x.

 Value of x 1 2 3 4 5 Probability 1/6= 0.1666667 (1/6)(5/6)=0.1388889 (1/6)(5/6)2=0.115741 (1/6)(5/6)3= 0.096551 (1/6)(5/4)4= 0.080376

We can easily calculate these (and more)probabilities on the TI-83 using the lists. We'll start by puttingthe first 50 values of x in list L1. Highlight L1 and thendo seq(x,x,1,50,1)->L1.

Now, we will put corresponding probabilities inL2. Highlight L2 and then do (1/6)*(5/6)^(L1-1). If you use1-Var Stats, youwill find that the sum of this column is .9998901152 (very close to1, as should be expected). This doesn't include the probabilities forgetting the first 6 on the 51st roll or more, but these are very,very close to 0.

Now highlight L3, and do L1*L2. The mean of the geometricrandom variable x will be very, very close to the sum of the numbersin L3. Using 1-Var Stats, the sum of this column is 5.99384645, which is very closeto 6.

We now note that the mean of a geometric variablex is given by the formula mx = 1/p. In this case, p = 1/6. Hence mx = 1/(1/6) = 6.

It would have been possible to use thegeometric distributionfunction on the TI-83 to do calculationsin this problem. Note that what will be written below "jives" withwhat appears above.

geometpdf(1/6,1) = .1666666667

geometpdf(1/6,3) =.1157407407

geometcdf(1/6,2) =.3055555556 (which is .1666666667 + .1388888889)

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Text:
The Practice of Statistics, by Yates, Moore, McCabe. New York,W.H. Freeman and Company, 1999. (ISBN 0-7167-3370-6)

Supplemental books:
The Cartoon Guide to Statistics, by Gonick and Smith. NewYork, HarperCollins Publishers, 1993. (ISBN 0-06-273102-5)
How to Lie with Statistics, by Darrell Huff. New York, W.W.Norton & Company, 1982 (ISBN 0-393-09426-X)