Generate Gaussian data in matlab

Question

I need to generate a Gaussian vector,e.g. "delta" -with arbitrary size-, with zero mean and variance of "alpha". If "alpha" is chosen such that norm(delta,2)<=0.5 with probability of e.g. 90%. How can we do that?

Answer 1

With var.*randn(1000,1) + mu you can generate a vector with a certain variance var and mean mu. Then we calculate the norm(delta,2). This operation is repeated 100000 times. In the variable B it is stored the values for which norm(delta,2)<=0.5. The probability is then Prob=length(B)/length(Normv)

mu = 0; alpha = 0.01537;
Normv=0;
REP=100000
for j=1:REP
    delta = alpha.*randn(1000,1) + mu;
    Normv(j)=norm(delta,2);
end
B=Normv(Normv<=0.5);
Prob=length(B)/length(Normv);

You could also include a for loop, sweeping the variance

Normv=0;
mu = 0; 
aux=1;
REP=10000;
variance = 0.014:0.0001:0.017;
for k=1:length(variance)
for j=1:REP
    delta = variance(k).*randn(1000,1) + mu;
    Normv(j)=norm(delta,2);
end
B=Normv(Normv<=0.5);
Prob(aux)=length(B)/length(Normv);
aux=aux+1;
end

plot(variance,Prob)
xlabel('Variance')
ylabel('Probability')

Here is the generated plot:

Plot Probability(Variance)

The alpha (variance) you are trying to find is 0.01537. The higher the REP the higher is the precision of your alpha.