Chapter6.1_6.2 lecture notes

# Chapter6.1_6.2 lecture notes - 6.1 POPULATIONS AND SAMPLES...

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6.1 POPULATIONS AND SAMPLES. 1. Finite population definition of a random sample of size n: A set of observations of X 1 , X 2 ….X n constitutes a random sample of size n from a finite population of size N , if its values are chosen such that the probability of each subset of n of the N elements of the population has the same probability of being selected. 2. Infinite population definition of a random sample. Each X i is a random variable with probability distribution given by f(x) (or pdf). The Xi are independent. 6.2 THE SAMPLING DISTRIBUTION OF THE SAMPLE MEAN,( σ KNOWN). 1. Theorem 6.1. If a random sample of n observations are taken and each of the X i have mean μ and standard deviation, σ . Then X , the average of these n values is a random variable (1) E( X ) = μ and (2) (i) Var( X ) = σ 2 /n if we have a sample from an infinite population and (ii) Var( X ) = ( σ 2 /n) 1 - - N n N if we have a random sample from a finite population . 2. Definition : Finite Population Correction Factor = 1 - - N n N .
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