# HP 49g+ User Manual Page 561

Graphing calculator.

f
(
x
)
The calculator provides for values of the upper-tail (cumulative) distribution
2
function for the χ
-distribution using [UTPC] given the value of x and the
parameter ν. The definition of this function is, therefore,
,
)
UTPC
x
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).
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) -
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
ν
x
1
1
x
e
2
2
ν
ν
2
(
)
2
2
t
(
)
1
(
f
x
dx
f
t
For example, UTPC(5, 2.5) =
,
ν
, 0
x
0
)
1
(
)
x
dx
P
X
x
(1 - UTPC(ν,a)) =
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