If one accepts this fact the proof is easy redplacing

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Unformatted text preview: ) = h(x)P (X = x) x (A.18) 216 APPENDIX A. REVIEW OF PROBABILITY When h(x) = x this reduces to EX , the expected value, or mean of X , a quantity that is often denoted by µ or sometimes µX to emphasize the random variable being considered. When h(x) = xk , Eh(X ) = EX k is the k th moment. When h(x) = (x E X )2 , Eh(X ) = E (X E X )2 = EX 2 (EX )2 2 is called the variance of X . It is often denoted by var (X ) or X . The variance is a measure of how spread out the distribution is. However, if X has the units of p then the variance has units of feet2 , so the standard deviation feet (X ) = var (X ), which has again the units of feet, gives a better idea of the “typical” deviation from the mean than the variance does. Example A.18. Roll one die. P (X = x) = 1/6 for x = 1, 2, 3, 4, 5, 6 so EX = (1 + 2 + 3 + 4 + 5 + 6) · 1 21 = = 3.5 6 6 In this case the expected value is just the average of the six possible values. EX 2 = (12 + 22 + 32 + 42 + 52 + 62 ) · 1 91 = 6 6 so the varianc...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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