Solution Found!
The number of breakdowns per week for a type of
Chapter 8, Problem 10E(choose chapter or problem)
The number of breakdowns per week for a type of minicomputer is a random variable Y with a Poisson distribution and mean \(\lambda \). A random sample Y1, Y2,..., Yn of observations on the
weekly number of breakdowns is available.
Suggest an unbiased estimator for\(\lambda \).The weekly cost of repairing these breakdowns is \(C=3 Y+Y^{2}\). Show that \(\mathrm{E}(\mathrm{C})=4 \lambda+\lambda^{2}\) Find a function of \(Y_{1}, Y_{2}, \ldots, Y_{n}\) that is an unbiased estimator of E(C). [Hint: Use what you know about \(\bar{Y} \text { and }(\bar{Y})^{2}\)
Equation Transcription:
Text Transcription:
\lambda
Y1, Y2,...,Yn
\lambda
C=3Y+Y2
E(C)=4\lambda + \lambda 2
Y1, Y2,...,Yn
\bar Y and ( \bar Y )2
Questions & Answers
QUESTION:
The number of breakdowns per week for a type of minicomputer is a random variable Y with a Poisson distribution and mean \(\lambda \). A random sample Y1, Y2,..., Yn of observations on the
weekly number of breakdowns is available.
Suggest an unbiased estimator for\(\lambda \).The weekly cost of repairing these breakdowns is \(C=3 Y+Y^{2}\). Show that \(\mathrm{E}(\mathrm{C})=4 \lambda+\lambda^{2}\) Find a function of \(Y_{1}, Y_{2}, \ldots, Y_{n}\) that is an unbiased estimator of E(C). [Hint: Use what you know about \(\bar{Y} \text { and }(\bar{Y})^{2}\)
Equation Transcription:
Text Transcription:
\lambda
Y1, Y2,...,Yn
\lambda
C=3Y+Y2
E(C)=4\lambda + \lambda 2
Y1, Y2,...,Yn
\bar Y and ( \bar Y )2
ANSWER:
Step 1 of 3
Given
The expected value and variance of a poisson distribution is equal to the value of the parameter
