Not sure what you mean by "one sequence correlated together with normal distribution"
You can generate a sequence that follows a particular normal distribution with randn()
For example, to generate a sequence that follows a N(0,1)
N = 1000;
x = randn(1000,1);
To generate a sequence that follows a N(mu,sigma^2) distribution
mu = 5;
sigma = 2;
x = mu+ 2*randn(1000,1);
These sequences will be white-noise sequences though. In other words, there will not be any autocorrelation (the individual sequence values will be mutually uncorrelated)
You can introduce any variety of autocorrelation by filtering the sequence. For example, to generate a lowpass AR(1) process.
A = [1 -0.9];
x = randn(1000,1);
y = filter(1,A,x);
The sequence y will show autocorrelation.
