2.1 Getting Started

The mathStatica package adds over a hundred new functions to Mathematica. But 95% of the time, we can get by with just 4 of them:

Table 0: Core functions for a random variable with density

This ability to handle plotting, expectations, probability, and transformations, with just 4 functions, makes the mathStatica system very easy to use, even for those not familiar with Mathematica.

To illustrate, let us suppose the continuous random variable has probability density function (pdf) , where . In Mathematica, we enter this as:

This is known as the Arc-Sine distribution. Here is a plot of :

Fig. 0: The Arc-Sine pdf

Here is the cumulative distribution function (cdf), , which also provides the clue to the naming of this distribution:

The mean, , is:

while the variance of is:

The moment of is :

The moment generating function (mgf) of is :

Now consider the transformation to a new random variable such that . By using the Transform and TransformExtremum functions, the pdf of , say , and the domain of its support can be found:

So, we have started out with a quite arbitrary pdf , transformed it to a new one , and since both density g and its domain have been inputted into Mathematica, we can also apply the mathStatica tool set to density .