* Let X,. X2, ..., X, be an independent sam- ple from a normal distribution with unknown mean u and variance o?. Show that the pair (X,5), where X=- x,. F' ='¿(x, – x). i=1 is a sufficient statistic for (u, o²). Given A> 0, consider AS as an estimator of o². For what values of A is AS (i) (ii) unbiased? maximum likelihood, Which value of A minimises the mean square error E(AS³ – o*)'?

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