Statistics Graduate Level Quiz
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A multinomial model has three cell probabilities p1=θp_1=\theta, p2=θ(1−θ)p_2=\theta(1-\theta), and p3=(1−θ)2p_3=(1-\theta)^2, where 0<θ<10<\theta<1. The observed cell counts are n1=12n_1=12, n2=8n_2=8, and n3=10n_3=10. What is the maximum likelihood estimate of θ\theta?
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