HP 49g manual MTH/PROB menu part, „´The Normal distribution, Student-t distribution

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 ∝ , 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(∝,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(∝,σ 2, x) = P(X>x) = 1 - P(X<x), where P() represents a probability. For example, check that for a normal distribution, with ∝ = 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

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