Forabinom(n, ) observation y, considertheBayesestimatorof using abeta(, ) prior distribution (a) Forlarge n, showthattheposteriordistributionof has approximatemean y n (It also hasapproximatevariance (1 ) n ) Interpret,andrelatetoclassicalinference (b) ShowthattheMLestimatorisalimitofBayesestimator...

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Forabinom(n, ) observation y, considertheBayesestimatorof using abeta(, ) prior distribution. (a) Forlarge n, showthattheposteriordistributionof has

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Forabinom(n, π) observation y, considertheBayesestimatorof π using abeta(α, β) prior distribution.

(a) Forlarge n, showthattheposteriordistributionof π has approximatemean ˆπ = y~n. (It also hasapproximatevariance ˆπ(1 − ˆπ)~n.) Interpret,andrelatetoclassicalinference.

(b) ShowthattheMLestimatorisalimitofBayesestimators,foracertainsequenceof α = β

values.

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