Central Limit Theorem for independent but non identically distributed random variables

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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 $\mu_i$.