Week_5_Practice_Problems

Week_5_Practice_Problems - Practice Problems Week...

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Practice Problems Week 5 (estimators and the Chi-squared Distribution) 1. Suppose we have a measurement system that is properly calibrated (i.e. on average gives the correct value) but possibly gives different values when the same unit is measured twice. Consider the following model for repeated measurement of the same unit , ~ (0, ) independent ii i YR R G τ σ =+ where is known to be 0.035 and represents the true value of the unit being measured. In using the system, 5 repeated measurements are taken and the average is used to estimate a) Write down the estimate algebraically and the corresponding estimator. b) How can you interpret this estimator? c) What is the probability the estimate is within 0.02 of the true value? d) What is the probability the estimator is within 0.02 of the true value? e) How many repeated measurements are required so that the user can be 95% certain that the estimator is within 0.01 of the true value?

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Week_5_Practice_Problems - Practice Problems Week...

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