Question: Please help me with solving questions ( a), ( b) and (c) . Provide all the steps to get to the final solution. Thanks a

Please help me with solving questions (a), (b) and (c). Provide all the steps to get to the final solution. Thanks a lot!

Let X1, X2, . . . , X11 denote an independent and identically distributed (i.i.d.) random sample from a random variable X with some unknown distribution F(X), with mean E(X,~) = ,u and liar-(Xi) = a2. (a) Write the expressions for the sample mean and sample variance. Are they unbiased estimators for ,u and 02, respectively? (b) Is the sample mean a consistent estimator for a? Explain. (C) Is the sample variance a consistent estimator for 0'2

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