Bias-variancetradeoff3: For n independentweightchangesinananorexiastudy,aresearcher believesitplausiblethat = 0 and toestimate decides tousetheestimator = cY for

Bias-variancetradeoff3: For n independentweightchangesinananorexiastudy,aresearcher believesitplausiblethat μ = 0 and toestimate μ decides tousetheestimator ˜μ = cY for a constant c with 0 ≤ c ≤ 1.

(a) Show that as c decreases from1to0,|bias|increasesbutvar(˜μ) decreases.

(b) FindMSE.Suppose μ = σ = n = 1. For c between0and1,plot(bias)2, var(˜μ), and MSE(˜μ). Find c to minimizeMSEanddescribehowthiswouldchangeas n increases.

(c) Explainhowtheestimate ˜μ = cy results fromaBayesian approachtoestimation.Explain the influenceof n on theextentofshrinkagetoward0.