Normal Distribution Cdf; The Student-t Distribution - HP 50g User Manual

Graphing calculator.

where
is the mean, and
value of f( , ,x) for the normal distribution, use function NDIST with the
following arguments: the mean, , the variance,
2
NDIST( ,
,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, ; the variance,
For example, check that for a normal distribution, with
UTPN(0.75) = 0.638163. Use UTPN(1.0,0.5,0.75) = 0.638163.
Different probability calculations for normal distributions [X is N( ,
defined using the function UTPN, as follows:
P(X<a) = 1 - UTPN(
P(a<X<b) = P(X<b) - P(X<a) = 1 - UTPN(
UTPN(
P(X>c) = UTPN(
Examples: Using
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 , known as the
degrees of freedom of the distribution. The probability distribution function (pdf)
is given by
2
is the variance of the distribution. To calculate the
2
; and, the value x, e.g., UTPN(( , ,x)
2
,a)
2
,a) - UTPN(
2
,c)
2
= 1.5, and
= 0.5, find:
2
,b)
2
, and, the value x , i.e.,
2
= 1.0,
2
,b) - (1 - UTPN(
= 0.5,
2
)] can be
2
,a)) =
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