Solution Found!
The joint distribution of amount of pollutant emitted from
Chapter 6, Problem 6E(choose chapter or problem)
The joint distribution of amount of pollutant emitted from a smokestack without a cleaning
device \(\left(Y_{1}\right)\) and a similar smokestack with a cleaning device \(\left(Y_{2}\right)\) was given in Exercise 5.10
to be
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll} 1, & 0 \leq y_{1} \leq 2,0 \leq y_{2} \leq 1,2 y_{2} \leq y_{1} \\ 0, & \text { elsewhere. } \end{array}\right.\)
The reduction in amount of pollutant due to the cleaning device is given by \(U=Y_{1}-Y_{2}\).
a Find the probability density function for U.
b Use the answer in part (a) to find E(U). Compare your results with those of Exercise 5.78(c).
Questions & Answers
(1 Reviews)
QUESTION:
The joint distribution of amount of pollutant emitted from a smokestack without a cleaning
device \(\left(Y_{1}\right)\) and a similar smokestack with a cleaning device \(\left(Y_{2}\right)\) was given in Exercise 5.10
to be
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll} 1, & 0 \leq y_{1} \leq 2,0 \leq y_{2} \leq 1,2 y_{2} \leq y_{1} \\ 0, & \text { elsewhere. } \end{array}\right.\)
The reduction in amount of pollutant due to the cleaning device is given by \(U=Y_{1}-Y_{2}\).
a Find the probability density function for U.
b Use the answer in part (a) to find E(U). Compare your results with those of Exercise 5.78(c).
ANSWER:Step 1 of 5
A joint probability density function (joint PDF) is a fundamental concept in probability theory and statistics, particularly in the field of multivariate probability distributions. It describes the likelihood of multiple random variables taking specific values simultaneously. The joint PDF is an extension of the concept of a probability density function, which characterizes the probability distribution of a single random variable.
Reviews
Review this written solution for 32037) viewed: 2388 isbn: 9780495110811 | Mathematical Statistics With Applications - 7 Edition - Chapter 6 - Problem 6e
Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.
No thanks, I don't want to help other students