Mean, Variance and Transforms
Part of the Undergraduate Texts in Mathematics book series (UTM)
The mathematical expectation of a random variable, defined in §4.3, is one of the foremost notions in probability theory. It will be seen to play the same role as integration in calculus—and we know “integral calculus” is at least half of all calculus. Recall its meaning as a probabilistically weighted average [in a countable sample space] and rewrite (4.3.11) more simply as:
$$E(X) = \mathop \Sigma \limits_\omega X(\omega )P(\omega )$$
KeywordsPower Series Independent Random Variable Mathematical Expectation Expected Number Multinomial Distribution
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© Springer Science+Business Media New York 1974