Simulation

We will now simulate some data from a normal 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 Normal(0, 1) distribution, but you are invited to change the parameters.

> restart: with(plots):

> mu:=0: sigma:=1: n:=500:

> sample:=NormalS(mu,sigma^2, n):

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

> num_bins:=32:

> a:=Histogram(sample,-4..4,num_bins):

> b:=plot(NormalPDF(mu,sigma^2,x),x=-4..4,color=black):

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

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

> theo_mean:=mu;

> sim_mean:=Mean(sample);

> difference:=sim_mean-theo_mean;

>