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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 (χ
2
) 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 µ ,
and variance σ
2
.
To calculate the value of probability density function, or pdf, of the f(x) for the
normal distribution, use function NDIST(µ,σ
2
,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(µ,σ
2
, x) = P(X>x) = 1 - P(X<x), where P()
represents a probability. For example, check that for a normal distribution,
with µ = 1.0, σ
2
= 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 ν, 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