Solution Found!
Use the results of Exercise 3.162 to find the mean and
Chapter 3, Problem 163E(choose chapter or problem)
Use the results of Exercise to find the mean and variance of a Poisson random variable with \(m(t)=e^{5\left(e^{t}-1\right)}\). Notice that \(r(t)\) is easier to differentiate than \(m(t)\) in this case.
Equation Transcription:
Text Transcription:
m(t)=e5(et-1)
r(t)
m(t)
Questions & Answers
QUESTION:
Use the results of Exercise to find the mean and variance of a Poisson random variable with \(m(t)=e^{5\left(e^{t}-1\right)}\). Notice that \(r(t)\) is easier to differentiate than \(m(t)\) in this case.
Equation Transcription:
Text Transcription:
m(t)=e5(et-1)
r(t)
m(t)
ANSWER:
Solution:
Step 1 of 4:
It is given that r(t)=ln[m(t)],and
=
.
Also, it is given that for a Poisson random variable m(t)=.
Using this we need to find the mean and variance of the Poisson random variable.