# Sampling Distribution Review

.ppt
1 Sampling Sampling Distributions Distributions Sampling Sampling Distributions Distributions
2 In real life calculating parameters of populations In real life calculating parameters of populations is prohibitive because populations are very large. is prohibitive because populations are very large. Rather than investigating the whole population, Rather than investigating the whole population, we take a sample, calculate a we take a sample, calculate a statistic statistic related to related to the the parameter parameter of interest, and make an of interest, and make an inference. inference. The The sampling distribution sampling distribution of the of the statistic statistic is the is the tool that tells us how close is the statistic to the tool that tells us how close is the statistic to the parameter. parameter.
3 Sampling Distribution of the Sampling Distribution of the Mean Mean An example An example A die is thrown infinitely many times. Let X A die is thrown infinitely many times. Let X represent the number of spots showing on represent the number of spots showing on any throw. any throw. The probability distribution of X is The probability distribution of X is x 1 2 3 4 5 6 p(x) 1/6 1/6 1/6 1/6 1/6 1/6 E(X) = 1(1/6) + 2(1/6) + 3(1/6)+ ......................= 3.5 V(X) = (1-3.5) 2 (1/6) + (2-3.5) 2 (1/6) + ............. ...= 2.92
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