B5. Let X1, X2, . . . ,Xn be IID random variable with common expectation ,u and common variance 02, and let I? = (X1+---+ Xn) be the mean of these random variables. We will be considering the random variable 32 given by 32 = 2m X)? i:1 (a) By writing or otherwise, show that (b) Hence or otherwise, show that You may use facts about X from the notes provided you state them clearly. (You may find it helpful to recognise some expectations as definitional formulas for variances, where appropriate.) (c) At the beginning of this module, we defined the sample variance of the values 2:1, 3:2, . . . ,xn to be 1 n 3;: \"1 2533753)? 7,: Explain one reason why we might consider it appropriate to use 1/(n 1) as the factor at the beginning of this expression, rather than simply l