The Chi-square Distribution - HP 50g User Manual

Graphing calculator.

where ( ) = ( -1)! is the GAMMA function defined in Chapter 3.
The calculator provides for values of the upper-tail (cumulative) distribution
function for the t-distribution, function UTPT, given the parameter and the value
of t, i.e., UTPT( ,t). The definition of this function is, therefore,
UTPT
For example, UTPT(5,2.5) = 2.7245...E-2. Other probability calculations for the
t-distribution can be defined using the function UTPT, as follows:
P(T<a) = 1 - UTPT( ,a)
P(a<T<b) = P(T<b) - P(T<a) = 1 - UTPT( ,b) - (1 - UTPT( ,a)) =
UTPT( ,a) - UTPT( ,b)
P(T>c) = UTPT( ,c)
Examples: Given
P(T<0.5) = 1-UTPT(12,0.5) = 0.68694..
P(-0.5<T<0.5) = UTPT(12,-0.5)-UTPT(12,0.5) = 0.3738...
P(T> -1.2) = UTPT(12,-1.2) = 0.8733...

The Chi-square distribution

The Chi-square (
freedom. The probability distribution function (pdf) is given by
(
2
f
) (
t
(
)
2
(
) ,
) (
t
f
t
= 12, determine:
2
) distribution has one parameter , known as the degrees of
1
f
(
x
)
2
2
1
)
2
t
1 (
)
t
1
) (
t
dt
f
x
1
x
e
2
2
(
)
2
1
,
t
2
1
(
t
dt
P
T
,
, 0
x
0
)
t
Page 17-11  