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Unformatted text preview: Chapter 7 Sampling Distributions 7.1 Random Sampling Recall: population consists of the all elements we are concerned and sample is a subset of a popu- lation. Now assume that the population has a probability density function f ( x ). Definition 7.1 A random sample of n , X 1 , X 2 , ··· ,X n , from population f ( x ) is a sequence of independent random variables , each having the same probability density function f ( x ) . That is, X 1 ,X 2 , ··· ,X n are independent and identically distributed (i.i.d.) random variables. For a given data set, we use x 1 ,x 2 , ··· ,x n to denote the random sample. Definition 7.2 Let X 1 ,X 2 , ··· ,X n be a random sample of size n . (i) The sample mean is defined by the statistic ¯ X = 1 n n X i =1 X i (ii) The sample variance is defined by the statistic S 2 = 1 n- 1 n X i =1 ( X i- ¯ X ) 2 . (iii) The sample standard deviation is defined by S = √ S 2 , the square root of the sample variance....
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