Simulation

We will now simulate some data from a t distribution in order to compare the sampling distribution to the theoretical distribution. The next bit of code will simulate a random sample of size 500 from a t (5) distribution, but you are encouraged to change the degrees of freedom.

> restart: with(plots):

> nu:=5: n:=500:

> sample:=TS(nu, n):

Remember that when you plot histograms, the number of bins that you select can make a huge difference in the plot.

> num_bins:=42:

> a:=Histogram(sample,-7..7,num_bins):

> b:=plot(TPDF(nu,x),x=-7..7,color=black):

> display([a,b],title="Simulated vs. Theoretical");

Now let's compare the simulated mean to the theoretical mean.

> theo_mean:=0;

> sim_mean:=Mean(sample);

> difference:=(sim_mean-theo_mean);