Solution Found!
Refer to Exercise 3.86. The maximum likelihood estimator
Chapter 3, Problem 87E(choose chapter or problem)
Refer to Exercise 3.86. The maximum likelihood estimator for \(p\) is \(1 / Y\) (note that \(Y\) is the geometric random variable, not a particular value of it). Derive \(E(1 / Y)\)
[Hint If \(|r|<1\), \(\sum_{i=1}^{\infty} r^{i} / i=-\ln (1-r)\).]
Equation Transcription:
Text Transcription:
p
1/Y
Y
E(1/Y)
|r|<1
sum over t=1 ^infty r^i/i=-ln(1-r)
Questions & Answers
QUESTION:
Refer to Exercise 3.86. The maximum likelihood estimator for \(p\) is \(1 / Y\) (note that \(Y\) is the geometric random variable, not a particular value of it). Derive \(E(1 / Y)\)
[Hint If \(|r|<1\), \(\sum_{i=1}^{\infty} r^{i} / i=-\ln (1-r)\).]
Equation Transcription:
Text Transcription:
p
1/Y
Y
E(1/Y)
|r|<1
sum over t=1 ^infty r^i/i=-ln(1-r)
ANSWER:
Solution :
Step 1 of 1:
Given we observe as the value for a geometric random variable Y.
Our goal is:
We need to derive .
Now we have to derive .
The maximum likelihood estimator for p=