HP 50G

Page 17-12
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,
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:
Θ P(X<a) = 1 - UTPC(
ν,a)
Θ P(a<X<b) = P(X<b) - P(X<a) = 1 - UTPC(
ν,b) - (1 - UTPC(ν,a)) =
UTPC(
ν,a) - UTPC(ν,b)
Θ 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
∫∫
∞−
∞
≤−=−==
t
t
xXPdxxfdxxfxUTPC )(1)(1)(),( ν
)
2
(
1
22
)1()
2
()
2
(
)()
2
(
)(
DN
NN
D
FNDN
F
D
NDN
xf
νν
νν
ν
ννν
ν
ννν
+
−
⋅
−⋅Γ⋅Γ
⋅⋅
+
Γ
=