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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….
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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).
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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
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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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