Stat400Lec15(Ch5.6) - STAT 400 Population Random Sample E(X...

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STAT 400 (Chapter 5.6) Spring 2012 Population: mean , standard deviation . Random Sample: X 1 , X 2 , … , X n . (or we say X i ’s are i.i.d.) E ( X 1 + X 2 + … + X n ) = n , SD ( X 1 + X 2 + … + X n ) = σ n . If the sampling is done without replacement from a finite population of size N , then SD ( X ) = 1 N N n n σ . The sample mean n n X ... X X 2 1 X . E ( X ) = , SD ( X ) = n σ . If the sampling is done without replacement from a finite population of size N , then SD ( X ) = 1 N N n n σ . X = + chance error. L AW OF L ARGE N UMBERS ( L AW OF A VERAGES ) : As the sample size, n , increases, the sample mean, X , “tends to gets closer and closer” to the population mean . For Bernoulli trials, as # of trials n increases, the sample proportion of “successes”, n X , “tends to gets closer and closer” to the probability of “success”
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C ENTRAL L IMIT T HEOREM:
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Stat400Lec15(Ch5.6) - STAT 400 Population Random Sample E(X...

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