# The F Distribution - HP 50g User Manual

Graphing calculator.

The calculator provides for values of the upper-tail (cumulative) distribution
function for the
parameter . The definition of this function is, therefore,
UTPC
To use this function, we need the degrees of freedom, , and the value of the
chi-square variable, x, i.e., UTPC( ,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( ,a)
P(a<X<b) = P(X<b) - P(X<a) = 1 - UTPC( ,b) - (1 - UTPC( ,a)) =
UTPC( ,a) - UTPC( ,b)
P(X>c) = UTPC( ,c)
Examples: Given
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 N = numerator degrees of freedom, and
D = denominator degrees of freedom. The probability distribution
function (pdf) is given by
2
-distribution using [UTPC] given the value of x and the
(
,
)
(
x
f
x
t
= 6, determine:
(
f
(
x
)
N
(
2
t
)
1
dx
f
N
D
N
)
(
2
D
D
)
(
)
1 (
2
(
)
1
(
x
dx
P
X
N
N
1
)
F
2
2
N
D
N
F
(
)
)
2
D
)
x
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