f(y) = (\theta + 1)y^{\theta}, \quad 0 < y < 1, \quad \theta > -1. (a) Derive the maximum likelihood estimator of \theta. Show all working.
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Step 1: The likelihood function for a sample of size $n$ is given by: $$L(\theta) = \prod_{i=1}^n f(y_i) = \prod_{i=1}^n (\theta + 1)y_i^\theta = (\theta + 1)^n \prod_{i=1}^n y_i^\theta$$ Show more…
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