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All of Statistics: A Concise Course in Statistical Inference

All of Statistics: A Concise Course in Statistical Inference. Chapter 3 Expectation Prepared by Gene Shiau. The average value of X. Also known as the expectation the mean the first moment The k th moment of X is. Properties of expectations.

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All of Statistics: A Concise Course in Statistical Inference

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  1. All of Statistics:A Concise Course inStatistical Inference Chapter 3 Expectation Prepared by Gene Shiau

  2. The average value of X • Also known as • the expectation • the mean • the first moment • The kth moment of X is

  3. Properties of expectations • If X1, ..., Xn are random variables and a1, ..., an are constants, then • If X1, ..., Xn are independent random variables, then

  4. The spread of X • Commonly measured using • the variance • If X has mean , the variance of X is • A well defined variance has the following properties:

  5. Sample statistics • The sample mean is • The sample variance is • Let X1, …, Xn be independent identically distributed, then

  6. The covariance and correlation • The covariance • The correlation

  7. Conditional expectation • The conditional variance is

  8. Laplace transform of X • Also known as • the moment generating function (MGF) • Properties:

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