HP 50G User Manual

Page 17-10
where μ is the mean, and σ
2
is the variance of the distribution. To calculate the
value of f(
μ,σ
2
,x) for the normal distribution, use function NDIST with the
following arguments: the mean,
μ, the variance, σ
2
, and, the value x , i.e.,
NDIST(
μ,σ
2
,x). For example, check that for a normal distribution, f(1.0,0.5,2.0)
= 0.20755374.
Normal distribution cdf
The calculator has a function UTPN that calculates the upper-tail normal
distribution, i.e., UTPN(x) = P(X>x) = 1 - P(X<x). To obtain the value of the
upper-tail normal distribution UTPN we need to enter the following values: the
mean,
μ; the variance, σ
2
; and, the value x, e.g., UTPN((μ,σ
2
,x)
For example, check that for a normal distribution, with
μ = 1.0, σ
2
= 0.5,
UTPN(0.75) = 0.638163. Use UTPN(1.0,0.5,0.75) = 0.638163.
Different probability calculations for normal distributions [X is N(
μ,σ
2
)] can be
defined using the function UTPN, as follows:
Θ P(X<a) = 1 - UTPN(
μ, σ
2
,a)
Θ P(a<X<b) = P(X<b) - P(X<a) = 1 - UTPN(
μ, σ
2
,b) - (1 - UTPN(μ, σ
2
,a)) =
UTPN(
μ, σ
2
,a) - UTPN(μ, σ
2
,b)
Θ P(X>c) = UTPN(
μ, σ
2
,c)
Examples: Using
μ = 1.5, and σ
2
= 0.5, find:
P(X<1.0) = 1 - P(X>1.0) = 1 - UTPN(1.5, 0.5, 1.0) = 0.239750.
P(X>2.0) = UTPN(1.5, 0.5, 2.0) = 0.239750.
P(1.0<X<2.0) = F(1.0) - F(2.0) = UTPN(1.5,0.5,1.0) - UTPN(1.5,0.5,2.0) =
0.7602499 - 0.2397500 = 0.524998.
The Student-t distribution
The Student-t, or simply, the t-, distribution has one parameter ν, known as the
degrees of freedom of the distribution. The probability distribution function (pdf)
is given by

HP 50G Specifications

General

Digits	33 digits
Battery type	CR2032
Type	Scientific
Form factor	Pocket

Weight and Dimensions

Weight	220 g
Dimensions (WxDxH)	87 x 184 x 23.5 mm