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variance Sis 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 mean1niixXn==∑. If the observed data are xi, i=1,….n, then the empirical distribution Feputs weight 1/n on each of the points x1,…..., xn(combining weight of i=1ninX1 nn2 ni=12 2i=1i=1n iii
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