Question: 4. Given a sample, {x1,x2,,xn}, from a Gaussian distributed random variable X with mean X, variance X2, and is not random; please answer the following

4. Given a sample, {x1,x2,,xn}, from a Gaussian distributed random variable

4. Given a sample, {x1,x2,,xn}, from a Gaussian distributed random variable X with mean X, variance X2, and is not random; please answer the following questions. (a) What is the sampling distribution of sample observation x2 ? (b) What is the sampling distribution of sample observation x5 ? (c) What is the sampling distribution of sample mean xn=i=1nxi ? (d) What is the sampling distribution of sample variance sX2=i=1n(xixn)2/(n1) ? (e) What is the sampling distribution of (n1)sX2/X2 ? (f) What is the sampling distribution of xn as the sample size n is large enough

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