Sec3.3_427

# Sec3.3_427 - Sect 3.3 Expected Values Summaries of prob...

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1 Sect. 3.3: Expected Values Summaries of prob. dist. Related to parameters Useful for theory In practice, we typically don’t know the parameters, but rather estimate them Let X be discrete RV with pmf p. The expected value of X or expectation of X or mean of X, m X is if finite. ) ( ] [ x xp X E x notation

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The Mean as a Measure of Location For (nearly) symmetric distributions, the mean is a measure of “center”: For “skewed” distributions, the mean is not a good measure of “center”:
3 Another Interpretation Suppose X 1 , X 2 , …, X n are independent RV’s having the same distribution. As n tends to infinity, in a sense made precise later. ) ( 1 X E n X n i i

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4 Functions of RV Often interested in functions of RV A function of a RV is a RV: Y = h(X) The expected value or expectation of h(X) is if finite Caution ) ( ) ( )] ( [ x p x h X h E x ]) [ ( )] ( [ X E h X h E
5 Useful Facts Note: All results require that expectations exist, but I

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## This note was uploaded on 03/22/2011 for the course STAT 427 taught by Professor Staff during the Spring '08 term at Ohio State.

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Sec3.3_427 - Sect 3.3 Expected Values Summaries of prob...

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