Reference Guide
3-266 Full Command and Function Reference
Input/Output:
Level 2/Argument 1 Level 1/Argument 2 Level 1/Item 1
n
x
→
utpc(n,x)
See also: UTPF, UTPN, UTPT
UTPF
Type: Command
Description: Upper Snedecor’s F Distribution Command: Returns the probability utpf(n
1
, n
2
, x) that a
Snedecor’s F random variable is greater than x, where n
1
and n
2
are the numerator and
denominator degrees of freedom of the F distribution.
The defining equations for utpf(n
1
, n
2
, x) are these:
•
For x ≥ 0:
n
1
n
2
-----
n
1
2
-----
Γ
n
1
n
2
+
2
-----------------
Γ
n
1
2
-----
Γ
n
2
2
-----
------------------------------
t
n
1
2–
2
--------------
x
∞
∫
1
n
1
n
2
-----
t+
n
1
n
2
+( )
2
-----------------------
–
dt
•
For x < 0:
u
t
p
f
n
1
n
2
x
,
,
(
)
1
=
For any value z,
Γ
z
2
---
z
2
--- 1–
!=
, where ! is the calculator’s factorial command.
The values n
1
and n
2
are rounded to the nearest integers and, when rounded, must be positive.
Access: !´
L
PROBABILITY
L
UTPF
( ´ is the left-shift of the Pkey).
Input/Output:
Level 3/Argument 1 Level 2/Argument 2 Level 1/Argument 3 Level 1/Item 1
n
1
n
2
x
→
utpf(n
1
,n
2
,x)
See also: UTPC, UTPN, UTPT
UTPN
Type: Command
Description: Upper Normal Distribution Command: Returns the probability utpn(m, v, x) that a normal
random variable is greater than x, where m and v are the mean and variance, respectively, of the
normal distribution.
For all x and m, and for v > 0, the defining equation is this:
utpn m v x, ,( )
1
2πv
-------------
e
t m–( )
2
2v
------------------–
td
x
∞
∫
=
For v = 0, UTPN returns 0 for x ≥ m, and 1 for x < m.
Access: !´
L
PROBABILITY
L
UTPN
( ´ is the left-shift of the Pkey).