Question: Practice midterm, no solutions. any help is appreciated! Q2 (12 points) Suppose Y1, Y2, ..., Yn are independent and identically distributed random variables with E(Y;)

Practice midterm, no solutions. any help is appreciated!

Q2 (12 points) Suppose Y1, Y2, ..., Yn are independent and identically distributed random variables with E(Y;) = M and Var(Yi) = 62. (a) [2 marks] Given that Var(Y) = E(Y2) - [E(Y)12, find E(Y,2). (b) [5 marks] Find E(Y), Var(Y) and E((Y)2). (c) [5 marks]Show that the sample standard deviation is an unbiased estimator of the population variance, i.e. show that n E [(x - 1) =02 or E : 02 n i=1 n i=1

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