Distributionshard
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Let XBinomial(100,0.01)X \sim \text{Binomial}(100, 0.01) and YPoisson(1)Y \sim \text{Poisson}(1). According to Le Cam's theorem, what is the upper bound on the total variation distance (expressed as the sum of absolute differences k=0P(X=k)P(Y=k)\sum_{k=0}^\infty |P(X=k) - P(Y=k)|) between the probability mass functions of XX and YY?