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

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-----1t 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
		-------------2πv
			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