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where \(e_t\) with mean of 0 and variance of \(\sigma^2\)

and |b| <1

Let \( a_k \) be a recursive sequence with \( a_1 \) =1 and \( a_{k+1} = a_k + P_k +1\) for \( k = 1, 2 ,...,\) where \(P_k \) is Poisson iid r.v with mean = 1

also, assume \(P_t\) and \(X_t\) are independent.

Is \(Y_k\)= \(X_{a_k}\) for k =1,2,... weakly stationary?

There arent any similar problems in the my textbook and i have no clue how to begin

Im not looking for a straight answer, just something to point me in the right direction.

Thanks in advance