1. Given a random sample, (8 ,I2,...,x }, from a random variable X with mean by and variance ox . please answer the following questions. (a) What is the mean of the sampling distribution of sample observation ry? (b) What is the variance of the sampling distribution of sample observation r;? (c) Are r2 and I, unbiased for ux? (d) Are r, and a consistent for ux? (e) What is the correlation between the sampling distributions of r, and ;? (f) What is the mean of the sampling distribution of sample mean In = )_, ;? (g) What is the variance of the sampling distribution of sample mean ? (h) Is a,, unbiased and consistent for ux? (i) Is the sample variance, sy = EM_(1, -2,)'/(n -1), unbiased and consistent for of? (j) What is the sampling distribution of z, as the sample size n is large enough? (k) What is the sampling distribution of to as n is large enough? f, is defined as In - HX