in my probability class I was given this question dealing with MATLAB code the purpose of which is to create and re estimate the random variables Z1, Z2, which reads as follows:
rng('default')
exps = 1e5;
sigX = 6;
sigY = 1;
% generate some normal (Gaussian) variables
X = sigX*randn(exps,1);
Y = sigY*randn(exps,1);
% generate a binary variable
B = rand(exps,1)>0.5;
% generate Z1 and Z2
Z1 = B.*X+(1-B).*Y;
Z2 = 0.5*(X + Y);
% display histograms (1st order distribution estimate)
subplot(211);
hist(Z1,1000)
xlabel('bins')
ylabel('frequency')
axis tight
subplot(212);
hist(Z2,1000)
xlabel('bins')
ylabel('frequency')
axis tight
And the output graphs are the following:
The question asks us to explain the results of these graphs (what is expected or not and so forth). We are also asked to relate this question to a previous result obtained which I already solved:
If two independent random variables X and Y which are independent from A which discretely receives one of two values {1,2} equally, defining the following random variable:
then we know the following information
And that the addition of two independent Gaussian variables is again Gaussian with sum of means and variances.
I have no idea how the MATLAB code works and how to relate the previous problem that I solved and how to explain the results so this is my problem, in explaining the results and relating the previous question. I thank all helpers out there