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

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

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 {}