- #1
peripatein
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Hi,
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.
The probability of i-th box being empty at the end is (1-1/m)n. Ergo, E[Xi] = P(Xi) = (1-1/m)n. Hence, E[X] = m(1-1/m)n.
As for the Variance, I used Var(Xi) = E[Xi](1-E[Xi])=(1-1/m)n(1-(1-1/m)n). Therefore, Var(X) = m*Var(Xi).
Is that correct?
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[Xi] = P(Xi) = (1-1/m)n. Hence, E[X] = m(1-1/m)n.
As for the Variance, I used Var(Xi) = E[Xi](1-E[Xi])=(1-1/m)n(1-(1-1/m)n). Therefore, Var(X) = m*Var(Xi).
Is that correct?