 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/discrete-mathematics-continuous-mathematics-and-probability/probability/7/b/i/solution

In the uniform balls-in-bins allocation, each ball enters box 1 independently with probability

1/ n

. Thus $M_{1}$ has the binomial distribution $Bin (n, 1/ n)$ , with probability mass function

P (M_{1} = k) = (k n) (\frac{1}{n})^{k} (1 - \frac{1}{n})^{n - k}, k = 0, \dots, n,

and zero outside that range.

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