Question: (i) For a counting r.v. \(X=\sum_{i=1}^{n} 1_{A_{i}}\), give a formula for the variance of \(X\) in terms of the probabilities \(P\left(A_{i}\right)\) and \(P\left(A_{i} \cap A_{j}\right), i \neq j\)

(ii) If \(k\) balls are put at random into \(n\) boxes, what is the variance of \(X=\) number of empty boxes?

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