Question: Suppose instead that you do not know if the die is weighted or not, so you roll it 100 times and collect a sample, .

Suppose instead that you do not know if the die is weighted or not, so you roll it 100 times and collect a sample, . You roll: 1 2 3 4 5 6 15 times 13 times 13 times 17 times 18 times 24 times a) What is an estimate for the mean of Y? b) What is the expected value of the estimator that you used in part (a)? Prove. c) What is an estimate for the variance of Y ( 2)? d) What is the variance of the estimator from part (a)? e) Write down the sampling distribution of the estimator from part (a). What desirable statistical properties does this estimator have? f) What is an estimator for the variance in part (d)? g) Test the null hypothesis that the mean of Y is equal to 3.5. What do you conclude about the fairness of the die

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