Hewlett-Packard F2226A - 48GII Graphic Calculator User's Manual
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Brand: HP
Category: Calculator
Type: Operation & user’s manual
Model: HP 48gII , HP F2226A - 48GII Graphic Calculator
Pages: 864 (9.97 Mb)
Page 17-12
0,0,
)
2
(2
1
)(
2
1
2
2
>>⋅⋅
Γ⋅
=
−−
xexxf
x
ν
ν
ν
ν
The calculator provides for values of the upper-tail (cumulative) distribution
function for the χ
2
-distribution using [UTPC] given the value of x and the
parameter ν. The definition of this function is, therefore,
∫∫
∞−
∞
≤−=−==
t
t
xXPdxxfdxxfxUTPC )(1)(1)(),(ν
To use this function, we need the degrees of freedom, ν, and the value of the
chi-square variable, x, i.e., UTPC(ν,x). For example, UTPC(5, 2.5) =
0.776495…
Different probability calculations for the Chi-squared distribution can be
defined using the function UTPC, as follows:
• P(X<a) = 1 - UTPC(ν,a)
• P(a<X<b) = P(X<b) - P(X<a) = 1 - UTPC(ν,b) - (1 - UTPC(ν,a)) =
UTPC(ν,a) - UTPC(ν,b)
• P(X>c) = UTPC(ν,c)
Examples: Given ν = 6, determine:
P(X<5.32) = 1-UTPC(6,5.32) = 0.4965..
P(1.2<X<10.5) = UTPC(6,1.2)-UTPC(6,10.5) = 0.8717…
P(X> 20) = UTPC(6,20) = 2.769..E-3
The F distribution
The F distribution has two parameters νN = numerator degrees of freedom,
and νD = denominator degrees of freedom. The probability distribution
function (pdf) is given by