Appendix B.pdf - Cambridge University Press

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714 Essential Mathematical Methods 3&4CASThe following screens demonstrate this syntax.6:fMin( and 7:fMax(These operations return the value for which the maximum or minimum value (or the leastupper bound or greatest lower bound) of a function occurs. fMax returns the value for which alocal maximum occurs only if this is the actual maximum for the interval being considered.A similar statement holds for fMin.The syntax for these functions is fMin(expression, var) and fMax(expression, var).A:nDeriv(This operation will produce the numerical derivative of a function by determiningf (x + h) − f (x − h). The derivative is then determined using the appropriate limit.hB:nInt(This returns an approximate value for a definite integral. This is illustrated in the followingscreens. In the screen to the left below the technique for integration discussed above isemployed for comparison.SAMPLECambridge University Press • Uncorrected Sample Pages •2008 © Evans, Lipson, Jones, Avery, TI-Nspire & Casio ClassPad material prepared in collaboration with Jan Honnens & David Hibbard
Appendix B—Computer Algebra System (TI calculators) 715B7ProbabilityPress 2ND MATH to obtain the MATH menu.Select 7: Probability to see the available functions.The first four are 1: !, 2:nPr(, 3:nCr( and 4:rand(The way of using 3:nCr( is to enter valuesof n and r as follows.In the home screen for 5 C 2 , enter nCr(5, 2)To generate a random integer between 1 and 6inclusive enter rand(6)For the binomial distribution, go to the Stats/List Editor(Application) and go to F5 to see the Distribution menu.Select B: Binomial Pdf. The screen appears as shown.Enter the value of p and n required. In the screenn = 6 and p = 0.7. Press ENTER again to see theprobability distribution.A better way to do this is to define a binomial function which can be kept.From F4 choose 1: Define and complete as bi(n, p, x) = nCr(n, x) ∗ p ∧ x ∗ (1 − p) ∧ (n − x);then this function can be used for any binomial distribution problem.Also for the cumulative distribution define the functioncbi(n, p, x) = (bi(n, p, x), x, 0, x). is found in the CALC menu.This will give the cumulative distribution. This is shown in the following section.For the normal distribution, go to the Stats/List editor (Application) and go to F5 to see theDistribution menu.Select 4: Normal Cdf.Enter the value of and required, for example = 6 and = 0.7. For Pr(X < 1) enterupper value = 1 and lower value =−∞. Press ENTER again to see the probability.Forinverse choose 1: Inverse Normal after choosing 2: Inverse from the F5 menu. Enterthe probability, and to obtain the result.Plotting a distributionSAMPLEThe example for the binomial distribution is used. In the Stats/List Editor the binomialdistribution values are found in the Pdf list. Enter 0 to 6 in List1. Press F2 plots and select PlotSetup. Select Plot1 and then press F1. Complete as shown. Press ENTER twice. Go to theGraph window and select 9. Zoom Data from the Zoom menu. The plot is as shown.Cambridge University Press • Uncorrected Sample Pages •2008 © Evans, Lipson, Jones, Avery, TI-Nspire & Casio ClassPad material prepared in collaboration with Jan Honnens & David Hibbard
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Appendix B.pdf - Cambridge University Press

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