Suppose you roll three 10-sided dice. Let X1, X2 and X3 the outcomes of the rolls of these three fair dice which can be viewed as a random sample of size 3 from a uniform distribution on integers. a) What is population from which these random samples are drawn? Find the mean () and variance of this population ( 2 )? Show your calculations and results on your Word file. 1 b) List all possible samples and calculate the value of the sample mean (X) and variance (s 2 ) for each sample? Show this work on your Excel file. c) Obtain the sampling distribution of X from this list by creating a frequency distribution table. Then calculate relative frequencies, i.e., f(x), which give the probabilities of the sampling distribution of X, and calculate the mean of the sampling distribution, i.e., xf(x). Check if that equals to (). Share these frequency and relative frequency tables on your Word file. d) Make a Histogram for the sampling distribution of X you have obtained in (c). Use the Data Analysis Toolpak in Excel to make the Histogram. For Bins, use the Row Labels of the frequency tables you have created in (c).