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

Command

 

 

 

Type:

 

 

 

Description:

Upper Snedecor’s F Distribution Command: Returns the probability utpf(n1, n2, x) that a

 

Snedecor’s F random variable is greater than x, where n1 and n2 are the numerator and

 

denominator degrees of freedom of the F distribution.

 

The defining equations for utpf(n1, n2, x) are these:

For x ≥ 0:

 

 

n1

Γ

n1 + n2

n1

-----

-----------------

2

 

 

 

 

 

2

-----

 

 

 

 

 

 

 

 

------------------------------

 

n2

 

Γ

n1

Γ

n2

 

 

 

 

-----

-----

 

 

 

 

2

 

2

 

 

 

 

 

 

 

 

 

 

n1 – 2

--------------

t 2

x

1+ n-----1t n2

( n1 + n2)

-----------------------

2

dt

• For x < 0:

 

 

 

 

 

 

 

 

utpf( n1, n2, x) = 1

 

 

 

 

 

Γ

--z=

--z

– 1

!

 

 

 

 

For any value z,

2

2

, where ! is the calculator’s factorial command.

 

 

 

 

 

 

 

 

 

The values n1 and n2 are rounded to the nearest integers and, when rounded, must be positive.

Access:

!´ LPROBABILITY LUTPF

( ´is the leftshift of the Pkey).

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 3/Argument 1

Level 2/Argument 2

Level 1/Argument 3

 

Level 1/Item 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

n1

 

 

 

n2

x

utpf(n1,n2,x)

 

 

 

 

 

 

 

 

 

 

See also:

UTPC, UTPN, UTPT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

UTPN

Command

 

 

 

 

 

 

 

 

 

Type:

 

 

 

 

 

 

 

 

 

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:

 

 

 

(t m)2

 

 

 

1

------------------2v

 

utpn(m, v, x)

=

e

 

dt

-------------v

 

 

 

 

x

 

 

 

 

 

 

 

 

 

 

For v = 0, UTPN returns 0 for x m, and 1 for x < m.

Access: !´ LPROBABILITY LUTPN

( ´is the leftshift of the Pkey).

3266 Full Command and Function Reference

Page 386
Image 386
HP 50g Graphing, 48gII Graphing manual Utpf, Utpn, UTPF, UTPN, Utpt, UTPC, UTPN, Utpt