# Utpn; Utpt - HP 48gII Advanced User's Reference Manual

Graphing calculator.

Description: Upper Snedecor ' s F Distribution Command: Returns the probability utpf(n
Snedecor ' s F random variable is greater than x, where n
denominator degrees of freedom of the F distribution.
The defining equations for utpf(n
• For x
• For x < 0:
For any value z,
The values n
!´ L
Access:
Input/Output:
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:
For v = 0, UTPN returns 0 for x m, and 1 for x < m.
!´ L
Access:
Input/Output:
UTPC, UTPF, UTPT

### UTPT

Type:
Command
Description: Upper Student ' s t Distribution Command: Returns the probability utpt(n, x) that a Student ' s t
random variable is greater than x, where n is the number of degrees of freedom of the
distribution.
The following is the defining equation for all x:
, n
1
0:
n
+
n
n
1
2
1
---------------- -
---- -
n
2
⎛ ⎞
2
1
---- -
------------------------------
⎝ ⎠
n
n
n
2
⎛ ⎞
⎛ ⎞
1
---- -
---- -
⎝ ⎠
⎝ ⎠
2
2
utp f n
z
z
⎛ ⎞
⎞ !
-- - ⎝ ⎠
=
-- -
1
2
2
and n
are rounded to the nearest integers and, when rounded, must be positive.
1
2
L
PROBABILITY
UTPF
Level 3/Argument 1
Level 2/Argument 2
n
1
utpn m v x
L
PROBABILITY
UTPN
Level 3/Argument 1
Level 2/Argument 2
m
and n
1
, x) are these:
2
n 1
+
---------------------- -
n
2
2
1
n
------------ - -
⎞ t
t
1
2
1
+
---- -
n
x
2
2
n
x
=
1
1
2
, where ! is the hp49g+/hp48gII factorial command.
( ´ is the left-shift of the Pkey).
Level 1/Argument 3
n
2
2
t m
------------------
1
2v
=
e
t d
-------------
2 v
x
( ´ is the left-shift of the Pkey).
Level 1/Argument 3
v
Full Command and Function Reference 3-193
, n
, x) that a
1
2
are the numerator and
2
n 2
dt
Level 1/Item 1
x
utpf(n
Level 1/Item 1
x
utpn(m,v,x)
,n
,x)
1
2

49g+