# Central Limit Theorem for independent but non identically distributed random variables

My question is the following:

Given the sum of R.V.s, $Z_N = X_1 + X_2 + ... +X_N$, where $X_i$ are independent, Rice distributed ($X_i\sim Rice(\mu_i,\sigma)$), is there any way to approximate $Z_N$ by a Gaussian distribution making use of the Central Limit Theorem?

$X_i$ have the same variance, but different mean $\mu_i$.

• Try Lyapunov's central limit theorem. Does your set up satisfy Lyapunov's condition? If so, the answer is yes. – David Simmons Sep 17 '14 at 10:01
• I suggest you work out whether the Liapounov condition is met. Recall, that the requirement is the r.v.'s are i.i.d. where the second "i" refers to identical be it whatever, in your case Rice. – Hirek Dec 19 '15 at 18:41