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# EVALUA~1 - Evaluating probability functions with calculator...

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Evaluating probability functions with calculator TI-83plus.doc May 7’09 Computing factorials, permutations, and combinations with TI-83plus calculator // see the file Perm_Comb_and_Probability_Distributions.doc * To compute n! , enter the whole number n in your calculator, then press the [MATH] key, select PRB with the right arrow key , then select 4: ! with the down arrow key ▼, and press the [ENTER] key twice . * To compute the number of permutations , n P r , enter the whole number n in your calculator, then press the [MATH] key, select PRB with the right arrow key , then select 2: n P r with the down arrow key ▼, and press the [ENTER] key. Then enter the whole number r and press the [ENTER] key. * To compute the number of combinations , n C r , enter the whole number n in your calculator, then press the [MATH] key, select PRB with the right arrow key , then select 3: n C r with the down arrow key ▼, and press the [ENTER] key. Then enter the whole number r and press the [ENTER] key. A. Evaluating of the Binomial probabilities with the calculator TI-83plus // See Handout_6a THE BINOMIAL DISTRIBUTION.doc and the Excel file // Three_Distributions.xls, sheet 1 For evaluating of the binomial probabilities P(x) = n C x p x (1 – p) n – x [see formula (6a.1) in Handout_6a ] p ress the keys: [2 nd ] [DISTR], then select 0: binompdf( with the up ( ) or down ( ) arrow key, and press the [ENTER] key. Then enter the numerical values of n (whole number) and probability p (0 p 1) separated by comma ( , ) and then, after the comma, enter in braces {} the sequence of whole values of x separated by commas ( , ) in accordance with the scheme: binompdf(n, p, {x 1 , x 2 , x 3 , …, x k }) and press the [ENTER] key. The sequence of probabilities computed for x 1 , x 2 , x 3 , …, x k appears in braces {}. Use the and arrow keys to read this sequence if necessary. Example A1. For evaluating of the probability P(x) = n C x p x (1 – p) n – x (6a.1) for n = 20, p = 0.75, x = 12 enter binompdf(20, .75, {12}) { .0608866892 } Answer 1

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For evaluating of the cumulative binomial probabilities x x x P(X ≤ x) = Σ P(i) = Σ n C i p i q n – i = Σ {n!/[i!(n – i)!]} p i q n – i (6a.5) i=0 i=0 i=0 press the keys: [2 nd ] [DISTR], then select A : binom c df( with the up ( ) or down ( ) arrow key, and press the [ENTER] key. Then enter the numerical values of n (whole number) and probability p (0 p 1) separated by comma ( , ) and then, after the comma, enter in braces {}
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