Consider a compound Poisson process ST=∑i=1NTXiS_T = \sum_{i=1}^{N_T} X_iST=∑i=1NTXi where NT∼Poisson(λT)N_T \sim \text{Poisson}(\lambda T)NT∼Poisson(λT) and Xi∼Uniform(0,1)X_i \sim \text{Uniform}(0, 1)Xi∼Uniform(0,1). What is the variance Var(ST)Var(S_T)Var(ST)?
λT/3\lambda T / 3λT/3
λT/6\lambda T / 6λT/6
λT/12\lambda T / 12λT/12
λT/2\lambda T / 2λT/2