Simple descriptive statistics
In Chapter 5, we implemented an Octave function mcintgr and its vectorized version mcintgrv. This function can evaluate the integral for a mathematical function f in some interval [a; b] where the function is positive. The Octave function is based on the Monte Carlo method and the return value, that is, the integral, is therefore a stochastic variable. When we calculate a given integral, we should as a minimum present the result as a mean or another appropriate measure of a central value together with an associated statistical uncertainty. This is true for any other stochastic variable, whether it is the height of the pupils in class, length of a plant's leaves, and so on.
In this section, we will use Octave for the most simple statistical description of stochastic variables.
Histogram and moments
Let us calculate the integral given in Equation (5.9) one thousand times using the vectorized version of the Monte Carlo integrator:
octave:4> for i=1:1000 >...
