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I have a question of computing the expectation of random sums.

E(sim_{k=1}^N X_k) = E(N)E(X) if N and X_1, X_2,.....are independent and X_k's are iid. Here both N and X_k's are r.vs.

But the condition of N and X_1, X_2,.....being independent is not true in many cases.

How will you compute E(sim_{k=1}^N X_k) if N and X_1, X_2,.....are not independent (even weakly dependent).

Can we use Law of iterative expectation? I am not sure what will E(sim_{k=1}^N X_k) equal to?

Please help.....

Thank you

Regards

Agrawal V

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# Expected value of random sums with dependent variables

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