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+ai +eijwhere eij ~ N(0,s ) for i = 1,…,I and j = 1,…,J.iid 2(a) Derive the MLEs of µ, ai, i = 1,…,I, and s2.(b) What are the MLEs of µ and s2 under the null hypothesis: H0 : a1 =a2 =…=aI =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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STATS 120C: Introduction to Probability and
Statistics III
Homework # 4
due Friday May 1, 2020 at 5:00PM
General instructions: If using R to answer questions, please include all code and
output in your problem solution.
1. Consider the one-way ANOVA model where
yi j = µ + ai + ei j
iid
where ei j ~ N(0, s2 ) for i = 1, . . . , I and j = 1, . . . , J.
(a) Derive the MLEs of µ, ai , i = 1, . . . , I, and s2 .
(b) What are the MLEs of µ and s2 under the null hypothesis: H0 : a1 =
a2 = . . . = aI = 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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