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h6 - Stat 5102(Geyer Spring 2012 Homework Assignment 6 Due...

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Stat 5102 (Geyer) Spring 2012 Homework Assignment 6 Due Wednesday, March 7, 2012 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 6-1. Suppose X 1 , X 2 , . . . , X n are IID Exp( λ ). Find the likelihood function and log likelihood function. 6-2. Suppose X 1 , X 2 , . . . , X n are IID Geo( p ). Find the likelihood function and log likelihood function. 6-3. Suppose X 1 , X 2 , . . . , X n are IID Cauchy( μ, σ ), where both μ and σ are unknown parameters. Find the likelihood function and log likelihood function. 6-4. Suppose X 1 , X 2 , . . . , X n are IID Laplace( μ, σ ), where both μ and σ are unknown parameters. Find the likelihood function and log likelihood function. 6-5. Suppose X 1 , . . . , X n are IID Exp( θ ) and Y 1 , . . . , Y n are IID Exp(1 ) and the X ’s and Y ’s are independent of each other. Find the likelihood function and log likelihood function.
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