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Lecture13_Chapter3

Lecture13_Chapter3 - Lecture 13 Chapter 3 Wednesday October...

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Lecture 13 – Chapter 3 Wednesday, October 8 th

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Moments The expected value of a power of a random variable is called moment (or moment around 0) First moment or Expected value E(X) Second moment E(X 2 ) Third moment E(X 3 ) and so on….
Central moments Central moment is the expected value of the difference a random variable and its expected value (or mean) to a power. It is also called moment about the mean. Second central moment : (or Variance) Third central moment : ( ) ( ) 2 E X μ ( ) ( ) 3 E X μ

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Moments and Central Moments Moments and central moments are useful because they give us useful information regarding the distribution of a random variable. Until now we know how to find the mean and the variance using moments and central moments. Another useful measure is skewness (see Chapter 1).
Skewness Skewness measures the departure from symmetry. Using the third and second central moments we can calculate skewness: ( ) ( ) 3 3 E X μ σ

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Example 3.26 page 118
Moment generating function Is not always easy to calculate moments and central moments. That’s why we use moment generating functions. The moment generating function (mgf) of a discrete random variable X is defined

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