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15Statistics - Statistics Jeffrey B Burl Click to edit...

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Click to edit Master subtitle style  EE 3180 Probability and  Statistics Jeffrey B. Burl 11
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 EE 3180 Probability and  Statistics n Statistics is the science of assembling,  classifying, tabulating, and analyzing  data or facts. n We will look at some basic sample  statistics: n The sample mean n Sample variance. 22
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 EE 3180 Probability and  The Sample Mean n Often, we do not know the mean of a  RV. n We can approximate this mean using  the average result in a large number of  independent trials. 33 1 1 ˆ n i i X X n = =
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 EE 3180 Probability and  The Mean of the Sample  Mean n Since the sample mean is a RV, we can  find its mean and variance: n Note that we assume that the N trials all  have the same probability density function,  and are all indendent. 44 [ ] 1 1 1 1 1 1 ˆ n n n i i i i i E X E X E X X X n n n = = = � � = = = = � � � �
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 EE 3180 Probability and  The Variance of the Sample  Mean n The variance of the sample mean is then: n Note that: 55 ( 29 2 2 2 2 2 1 1 1 1 1 ˆ n n n i i j i i j E X X E X X E X X X n n = = = - = - = - �� 2 2 1 1 1 n n i j i j E X X X n = = = - �� [ ] ( 29 2 2 2 i j E X i j E X X E X X i j i = ° = =
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