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If I'm selecting $N$ elements uniformly at random (with replacement) from $\{1, \dots, M\}$, what is the expected number of values that are selected exactly once?

The basis for this question originated here.

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Hint: Expected value is linear. What is the probability that a particular value is selected exactly once?

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  • $\begingroup$ Is that $$\Big({M-1\over M}\Big)^{N-1} \;\;\;\; ?$$ $\endgroup$ – Aqua Nov 2 '17 at 19:30

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