Question: 1. Given a random sample, {x1,x2,,xn}, from a random variable X with mean X and variance X2, please answer the following questions. (a) What is

1. Given a random sample, {x1,x2,,xn}, from a random variable X

1. Given a random sample, {x1,x2,,xn}, from a random variable X with mean X and variance X2, please answer the following questions. (a) What is the mean of the sampling distribution of sample observation x2 ? (b) What is the variance of the sampling distribution of sample observation x5 ? (c) Are x2 and x5 unbiased for X ? (d) Are x2 and x5 consistent for X ? (e) What is the correlation between the sampling distributions of x2 and x5 ? (f) What is the mean of the sampling distribution of sample mean xn=i=1nxi ? (g) What is the variance of the sampling distribution of sample mean xn ? (h) Is xn unbiased and consistent for X ? (i) Is the sample variance, sX2=i=1n(xixn)2/(n1), unbiased and consistent for X2 ? (j) What is the sampling distribution of xn as the sample size n is large enough? (k) What is the sampling distribution of txn as n is large enough? txn is defined as txn=nsX2xnX

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