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Distributionshard
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Let Z1,Z2,…,ZnZ_1, Z_2, \dots, Z_nZ1​,Z2​,…,Zn​ be i.i.d. Bernoulli(p)(p)(p) trials. Define X=∑i=1kZiX = \sum_{i=1}^{k} Z_iX=∑i=1k​Zi​ and Y=∑i=mnZiY = \sum_{i=m}^{n} Z_iY=∑i=mn​Zi​, where 1<m≤k<n1 < m \le k < n1<m≤k<n. What is the covariance between XXX and YYY?