Suppose X is a random variable with population mean µX. Suppose we observe a random sample of X and estimate µX with the sample average X¯ = PN i=1 Xi . The law of large numbers says that

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1. Suppose X is a random variable with population mean µX. Suppose we observe a random sample of X and estimate µX with the sample average X¯ = PN i=1 Xi . The law of large numbers says that


[a] The value of µ will get larger and larger as the sample size increases. 


[b] As the sample size increases, the sample average and the value of µX will get larger and larger. 


[c] The population mean of the sample average will get closer and closer to µX as the sample size increases. 


[d] As the sample size increases, the sample average will converge in probability to µX. 


[e] none of the above



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