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3192概率中等derivationmedium

Aggregate Slippage Over a Poisson Number of Orders

题目

Let X1,X2,X_1,X_2,\dots be i.i.d. increments with E[Xi]=2E[X_i]=2 and Var(Xi)=3\mathrm{Var}(X_i)=3. Let NN be independent of the increments and distributed as Poisson(4). For the stopped sum SN=i=1NXiS_N=\sum_{i=1}^N X_i, compute E[SN]E[S_N] and Var(SN)\mathrm{Var}(S_N).

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你的答案

E[S_N]

Var(S_N)