Solution Found!
Refer to Exercise 3.64. The maximum likelihood estimator
Chapter 3, Problem 65E(choose chapter or problem)
Refer to Exercise 3.64. The maximum likelihood estimator for p is \(Y / n\) (note that Y is the
binomial random variable, not a particular value of it).
a Derive \(E(Y / n)\). In Chapter 9, we will see that this result implies that \(Y / n\) is an unbiased
estimator for p.
b Derive \(V(Y / n)\). What happens to \(V(Y / n)\) as n gets large?
Equation Transcription:
Text Transcription:
Y/n
E(Y/n)
Y/n
V(Y/n)
V(Y/n)
Questions & Answers
QUESTION:
Refer to Exercise 3.64. The maximum likelihood estimator for p is \(Y / n\) (note that Y is the
binomial random variable, not a particular value of it).
a Derive \(E(Y / n)\). In Chapter 9, we will see that this result implies that \(Y / n\) is an unbiased
estimator for p.
b Derive \(V(Y / n)\). What happens to \(V(Y / n)\) as n gets large?
Equation Transcription:
Text Transcription:
Y/n
E(Y/n)
Y/n
V(Y/n)
V(Y/n)
ANSWER:
Solution:
Step 1 of 3:
It is given that Y denotes the number of people who favour the new policy among 20 people.
Y has the Binomial distribution with n=20 and probability of success p.
Then,
P(Y=y)=
Also, it is given that is the maximum likelihood estimator of p.
Using this, we need to find the required estimates.