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## Homework Statement

n different balls are distributed independently between m boxes with unlimited capacity each. I am asked to find the expectation and variance of the number of empty boxes.

## Homework Equations

## The Attempt at a Solution

The probability of i-th box being empty at the end is (1-1/m)

^{n}. Ergo, E[X

_{i}] = P(X

_{i}) = (1-1/m)

^{n}. Hence, E[X] = m(1-1/m)

^{n}.

As for the Variance, I used Var(X

_{i}) = E[X

_{i}](1-E[X

_{i}])=(1-1/m)

^{n}(1-(1-1/m)

^{n}). Therefore, Var(X) = m*Var(X

_{i}).

Is that correct?