Question

1. You collect the following sample of size 10 from a process of unknown distribution, and you are asked to find the best estimate you can for the true mean u of the distribution according to what you know about point estimation. 56.1 53.5 72.8 65.9 66.4 44.8 76.0 63.761.2 56.6 a.) First, someone tells us the underlying distribution is normal. Assuming this person is correct, what is your estimate of μ? b.) A second expert tells us that the underlying distribution is the Cauchy If this person is correct, what is your estimate of u? C) A third person tells us the distribution is uniform. If this person is correct, what is your estimate of i? d.) You finally decide that since all the "experts" are telling us different things about the shape of the distribution, it is probably the sad truth that no one really knows for sure. You therefore decide to settle on a safe compromise solution as an estimate for u. What might that be? e.) Later, you find you also need to estimate the standard deviation ơof the distribution. What is your estimate for that? Is that an unbiased estimate for σ? Is it a reasonable estimate for σ anyway?

Please show how you get the final answer, with work and formulas. Please , solve b to e. Thank you!

Answer 1

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