A person’s birthday occurs on a day i with probability P i , where i = 1, ..., n. (Of course, P 1 + ... + P 2 = 1.) Assume independent assignment of birthdays among different people. In a room with k people, let P k = P k (p 1 , ..., p n ) be the probability that no two persons share a birthday. Show that this probability is maximized when all birthdays are equally likely: p i = 1/n ∀i.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A person’s birthday occurs on a day i with probability P i , where i = 1, ..., n. (Of course, P 1 + ... + P 2 = 1.) Assume independent assignment of birthdays among different people. In a room with k people, let P k = P k (p 1 , ..., p n ) be the probability that no two persons share a birthday. Show that this probability is maximized when all birthdays are equally likely: p i = 1/n ∀i.
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