- #1
agarwalv
- 3
- 0
Hi all,
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
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