how to generate two uncorrelated gaussian random variables

i tried to generate two uncorrelated random process which i tried like this

x1=random('Normal',0,1,1,N);
x2=random('Normal',0,0.5,1,N);

is this right. pls help me. thanks in advance

Answer 1

[the cyclist]

That is one way to generate uncorrelated random normals.

Another would be to use the randn() command.

[Kavya]

are all the variables generated using the randn() function be uncorrelated ? in case of generating a random channel matrix whose values must be uncorrealted ?

[Walter Roberson]

format long g
N = 1e7;
X = randn(N,1);
Y = randn(N,1);

R = corrcoef(X, Y)

R = 2×2

1 -0.000347360611933317 -0.000347360611933317 1

The anti-diagonal is not zero, but it is not large either.

The default random number generator MT19937 has a very long period, and are considered to pass the https://en.wikipedia.org/wiki/Diehard_tests

This does not mean that values from randn() are completely uncorrelated -- but the correlation is low. For example it would not astonish me if the correlation were on the order of 2^-sqrt(19937) which would be roughly 3.8 * 10^-43

[the cyclist]

@Kavya, be aware that finite samples from two independent parent distributions will typically have some correlation. It is essentially a type of sampling error.

This is a similar phenomenon, conceptually, to tossing N fair coins and realizing that you would not expect exactly N/2 heads every time.