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Distributionshard
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Consider a compound Poisson process St=∑i=1NtXiS_t = \sum_{i=1}^{N_t} X_iSt​=∑i=1Nt​​Xi​, where Nt∼Poisson(λt)N_t \sim \text{Poisson}(\lambda t)Nt​∼Poisson(λt) and Xi∼Exp(β)X_i \sim \text{Exp}(\beta)Xi​∼Exp(β). What is the variance of StS_tSt​?