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349Robust Variance of a Random Sum (Wald's Variance Identity)A shop receives N customer orders per day, where N \sim Poisson (8). Each order has an independent random dollar amount X i with E[X i] = 50 and Var (X i) = 400. Let S = X 1 + X 2 + \cdots + X N be the total daily revenue. Using the law of total variance, derive a formula for Var (S) and evaluate it. Additional robustness twist: before observation, an independent random relabeling of outcome labels is applied. Compute the same target and justify invariance.概率中等数值题未尝试免费5982Variance of Fills Over a Binomial Number of QuotesOut of n=10 resting quotes, each fills independently with probability 0.3, so the number of fills N is Binomial(10,0.3). Each fill produces an i.i.d. PnL X i with E[X i]=2 and Var (X i)=9, independent of which quotes fill. For the stopped sum S N=\sum i=1 N X i, compute Var (S N).概率中等derivation未尝试免费