Concept explainers
Let Y1, Y2, … , Yn denote a random sample from a
a If μ is unknown and σ2 is known, show that
b If μ is known and σ2 is unknown, show that
c If μ and σ2 are both unknown, show that
a.
Prove that if µ is unknown and
Answer to Problem 38E
It is proved that if µ is unknown and
Explanation of Solution
Let
The likelihood function is given as follows:
Where
By Theorem 9.4 (Factorization theorem), it can be said that if µ is unknown and
b.
Prove that if µ is known and
Answer to Problem 38E
It is proved that if µ is known and
Explanation of Solution
The likelihood function is given as follows:
Where
By Theorem 9.4 (Factorization theorem), it can be said that if µ is known and
c.
Prove that if both µ and
Answer to Problem 38E
It is proved that if both µ and
Explanation of Solution
The likelihood function is given as follows:
Where
By Theorem 9.4 (Factorization theorem), it can be said that if both µ and
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Chapter 9 Solutions
Mathematical Statistics with Applications
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