Derive a formula for the estimator sigma using the map, Project Management

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Derive a formula for the estimator sigma using the map

In this problem, we address the issue of estimating the standard deviation s of a Gaussiandistributed random variable X of zero mean. The standard deviation itself is uniformly distributed inside the interval [σ₁,σ₂].

For the estimation, we have N independent observations of the random variable X, namely

1137_Equation 04.jpg

a. Derive a formula for the estimator σ using the MAP rule.

b. Repeat the estimation using the maximum likelihood criterion.

c. Comment on the results of parts a and b.

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Project Management: Derive a formula for the estimator sigma using the map

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Project Management: Derive a formula for the estimator sigma using the map

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