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2. (a) Two objects with unknown weights μ1 and μ2 are weighed separately on a scale and together (both placed on the scale), giving three measurements15.6,r2 29.3 and r 45.8. It is known from previous experience with the scale that measurements are independent and normally distributed about the true weights with variance 1 Determine the maximuin likelihood estimates of 111 and μ2. (b) Suppose that ri,..., In are a random sample of lifetimes for individuals diagnosed with a certain disease. Assume a model with where k is fixed and known Interest is in the parameter -P(X > 25; A) which gives the probability that an individual will survive more than 25 years with the disease. It can be shown that the cumulative distribution Determine the MLE of C
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