A shipment of 1000 sacks of oranges arrives at a distribution centre in Edinburgh, one of 10 such facilities in Scotland. The sender quotes a nominal weight of 20 kg and a standard deviation of no more than 2000 g per sack. A random sample of 10 sacks is selected and weighed, giving a mean of = 20.77 kg and variance S2 = 4.85 kg². Throughout this exercise you should assume a Gaussian model for the data. (a) Show that the sample mean coincides with the maximum likelihood estimator (MLE) for while the sample variance differs from the MLE for o2. Why is the MLE for the μ variance not the preferred choice for small samples?

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