The autocorrelation function of i.i.d process

Question

$\{x(n)\}$ is i.i.d; therefore, it is strictly stationary.
Can I say the autocorrelation function $\{x(n)\}$ is a delta function, that is $R_X[k] = N_0\delta(k)$?

Thanks

Answer 1

I try to answer my question:

If $\{X(k)\}$ i.i.d, we can say $C_X[k] = N_0\delta(k)$. But not vice versa.
Except, $C_X[k] = N_0\delta(k)$ and $\{X(k)\}$ is Gaussian, by which we can say it is i.i.d.

The key thing here is $C_X[k] = N_0\delta(k)$ means uncorrelated but not independent except for Gaussian.