M4L5
Expectation and Moments of Functions of Random Variable
1.
Introduction
This lecture is a continuation of previous lecture, elaborating expectations, moments and
moment generating functions of the ‘functions of random variable’ discussed earlier.
2.
Moments of functions of random variables
In general, the
th
moment of the function of discrete random variable
is given by:
And the
th
moment of the function of continuous random variable
is given by:
2.1.
Moments of functions of random variables about its mean
The
th
moment of the function of discrete random variable
about its mean is given
by:
The
th
moment of the functions of continuous functions
is expressed as:
2.2.
Variance of discrete functions
The variance of discrete function,
is expressed as:

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