Question

Suppose X has a binomial distribution with parameters n & p. For what p is var(X) maximized if we assumed n is fixed?

Answer 1

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In probability theory and statistics, the binomial distribution with parameters n and pis the discrete probability distribution of the number of successes in a sequence of nindependent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: a random variable containing a single bit of information: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q = 1 − p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.

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