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3. Suppose X has the following density function: fX(x)=θxθ−1,0≤x≤1 for some parameter θ. (a) What is the MLE for θ base
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3. Suppose X has the following density function: fX(x)=θxθ−1,0≤x≤1 for some parameter θ. (a) What is the MLE for θ base
3. Suppose X has the following density function: fX(x)=θxθ−1,0≤x≤1 for some parameter θ. (a) What is the MLE for θ based on a random sample Xi,1≤i≤n, from this distribution? (b) Show that the likelihood ratio is monotone (increasing or decreasing) in Πi=1nXi for any pair of θ0 and θ1. (c) What is the LRT for the case H0:θ=θ0 versus H1:θ=θ1. Consider the two cases, one where θ0>θ1 and the other where θ0<θ1. (d) Design in detail such a test for a given significance level of α in the case where n=1.
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