Variance s is an unbiased estimator of population

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variance S is an unbiased estimator of population variance σ . (10 marks) 11. For any set at number x , ….., x prove algebraically that ( x – x ) = x - n x where x = x /n . (10 marks) 12. Write a method for determining when to stop generating new data to estimate a population mean. (10 marks) 13. Write a procedure for determining when to stop generating new values to estimate a probability. (The data values are Berroulli random variables). (10 marks) 14. If the first three data values are X1=5, X2=14, X3=9, and then find their sample mean and simple variance. (10 marks) 15. Suppose we are interested in estimating θ (F) =E[X] by using the sample mean 1 n i i x X n = = . If the observed data are x i , i=1,….n, then the empirical distribution F e puts weight 1/n on each of the points x 1 ,…..., x n (combining weight of i=1 n i n X 1 n n 2 n i= 1 2 2 i= 1 i= 1 n i i i
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