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This document provides an introduction to moment generating functions and characteristic functions in probability theory. [1] It defines the moment generating function (MGF) as the expected value of e raised to the power of t multiplied by the random variable, where t is in some interval I where the expectation exists. [2] The MGF uniquely identifies a distribution unlike moments alone. [3] Properties of MGFs include that shifting or scaling a random variable shifts or scales its MGF, and the MGF of a sum o

Author

arjunvenugopalachary

Language

EN