Distributionshard
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Let Z1,Z2,,ZnZ_1, Z_2, \dots, Z_n be i.i.d. Bernoulli(p)(p) trials. Define X=i=1kZiX = \sum_{i=1}^{k} Z_i and Y=i=mnZiY = \sum_{i=m}^{n} Z_i, where 1<mk<n1 < m \le k < n. What is the covariance between XX and YY?