STAT 100B HW 8 Due Friday Problem 1: Suppose Y ∼ Bernoulli( λ ). Suppose [ X | Y = 0] ∼ N( μ0 ,σ 2 ), and [ X | Y = 1] ∼ N( μ 1 ,σ 2 ). (1) Find the marginal density of X . Explain your result intuitively. (2) Calculate Pr( Y = 1 | X = x ). Explain your result intuitively. (3) Show that log[Pr( Y = 1 | X = x ) / Pr( Y = 0 | X = x )] = β0 + β 1 x , where β0 and β 1 can be calculated from λ , μ 1 , μ0 , σ 2 . Problem 2: Suppose Y i ∼ Bernoulli( λ ) independently, for i = 1 ,...,n . Suppose [ X i | Y i = 0] ∼ N( μ0 ,σ 2 ), and [ X i | Y i = 1] ∼ N( μ 1 ,σ 2 ). Find the maximum likelihood estimates of λ , μ 1 , μ0 , σ 2 . Problem 3: In the following data set, the ﬁrst column records
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This note was uploaded on 03/30/2011 for the course STAT 100B taught by Professor Wu during the Spring '11 term at UCLA.