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1) Suppose X1, X2, X3, Xn and Y1, Y2, Y3, Ym are independent random samples from N (14,02) and N (122,02), respectively. Suppose n=10, m= 12, the sample means are 10 and 15, respectively, and the sample variances are 9 and 16, respectively. Let Z=3X 2Y. Assuming the true variances are not equal, estimate the variance of Z and its degrees of freedom, and find an expression for the 95% confidence interval for E[Z]. 2) X1, X2, X3, , Xn is a random sample from N(0,1). Show that X2-115 the best unbiased estimator of 02. 3) Suppose X1, X2, X3, , Xn is a random sample from a Bernoulli(p) distribution. Show that the variance of X attains the Crámer-Rao lower bound.

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