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Bernoulli Trials, Poisson Trials, Surprising Variances, and Jensen's Inequality
Jerry Nedelman and Ted Wallenius
The American Statistician
Vol. 40, No. 4 (Nov., 1986), pp. 286-289
Stable URL: http://www.jstor.org/stable/2684605
Page Count: 4
You can always find the topics here!Topics: Statistical discrepancies, Random variables, Experimentation, Binomials, Statistics, Binomial distributions, Integers, Intuition, Maximality
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Let X be the number of successes in n independent dichotomous trials. Among all sets of success probabilities (p1,..., pn) with a given average p̄, X has maximal variance when p1 = p2 = ⋯ = pn, = p̄. Many authors have called this fact surprising. We suggest how to exploit the surprise to lead first-year probability students through a discussion about convex functions, Jensen's inequality, and compound distributions.
The American Statistician © 1986 American Statistical Association