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The Mth/prob Menu - Part 2; The Normal Distribution; The Student-t Distribution - HP 50g User Manual

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The MTH/PROB menu - part 2

In this section we discuss four continuous probability distributions that are
commonly used for problems related to statistical inference: the normal
distribution, the Student's t distribution, the Chi-square (
) distribution, and
the F-distribution. The functions provided by the calculator to evaluate
probabilities for these distributions are NDIST, UTPN, UTPT, UTPC, and
UTPF. These functions are contained in the MTH/PROBABILITY menu
introduced earlier in this chapter. To see these functions activate the MTH
menu: „´ and select the PROBABILITY option:

The Normal distribution

Functions NDIST and UTPN relate to the Normal distribution with mean
and variance
To calculate the value of probability density function, or pdf, of the f(x) for
the normal distribution, use function NDIST( ,
, x). For example, check
that for a normal distribution, NDIST(1.0, 0.5, 2.0) = 0.20755374. This
function is useful to plot the Normal distribution pdf.
The calculator also provides function UTPN that calculates the upper-tail
normal distribution, i.e., UTPN( ,
, x) = P(X>x) = 1 - P(X<x), where P()
represents a probability. For example, check that for a normal distribution,
= 1.0,
= 0.5, UTPN(1.0, 0.5, 0.75) = 0.638163.

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 calculator provides for
values of the upper-tail (cumulative) distribution function for the t-
distribution, function UTPT, given the parameter
and the value of t, i.e.,
UTPT( ,t) = P(T>t) = 1-P(T<t). For example, UTPT(5,2.5) = 2.7245...E-2.
Page 15-3


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