Quantitative Research Intern Interview Questions

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A person’s birthday occurs on a day i with probability pi, where i = 1, . . . , n. Assume independent assignment of birthdays among different people. In a room with k people, let Pk = Pk(p1, . . . , pn) be the probability that no two persons share a birthday. Show that this probability is maximized when all birthdays are equally likely: pi = 1/n for all i.
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Quantitative Analyst

Interviewed at Huatai Securities

3.4
Sep 20, 2018

A person’s birthday occurs on a day i with probability pi, where i = 1, . . . , n. Assume independent assignment of birthdays among different people. In a room with k people, let Pk = Pk(p1, . . . , pn) be the probability that no two persons share a birthday. Show that this probability is maximized when all birthdays are equally likely: pi = 1/n for all i.

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