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September 11, 2020

3 Questions of Intro to Stat and ProbabilitiesQuestion 2 is

3 Questions of Intro to Stat and ProbabilitiesQuestion 2 is in attached filesGeneral instructions: If using R to answer questions, please include all code and output in your problem solution.1. Consider the one-way ANOVA model whereyij = μ+αi +εijwhere εij ∼ N(0,σ ) for i = 1,…,I and j = 1,…,J.iid 2(a) Derive the MLEs of μ, αi, i = 1,…,I, and σ2.(b) What are the MLEs of μ and σ2 under the null hypothesis: H0 : α1 =α2 =…=αI =0? 2. Problem 13.18 from J. Rice “Mathematical statistics and data analysis” page 536.3. In professional basketball games during 1980-1982, when Larry Bird of the Boston Celtics shot a pair of free throws, 5 times he missed both, 251 times he made both, 34 times he made only the first, and 48 times he made only the second. Is it plausible that the successive free throws are independent?

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