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Exercise 5.1.11

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$m = 0 p_{0} + 1 p_{1} + \dots + N p_{N} = \sum_{i} i p_{i} = \sum_{i} \frac{i b_{i}}{2^{N}} = \frac{1}{2^{N}} \sum_{i} i b_{i} = \frac{1}{2^{N}} \sum_{i} i \frac{N!}{i! (N - i)!} = \frac{1}{2^{N}} \sum_{i} \frac{N!}{(i - 1)! (N - i)!} = \frac{N}{2^{N}} \sum_{i} \frac{(N - 1)!}{(i - 1)! (N - i)!} = \frac{N}{2^{N}} 2^{N - 1} = \frac{N}{2}$

niuers

2020-03-20 00:00

Exercise 5.1.11

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