## Solution for problem 5.78 Chapter 5

# In Exercise 5.10, we proved that f (y1, y2) = $ 1, 0 y1 2, 0 y2 1, 2y2 y1, 0, elsewhere

Mathematical Statistics with Applications | 7th Edition

In Exercise 5.10, we proved that f (y1, y2) = $ 1, 0 y1 2, 0 y2 1, 2y2 y1, 0, elsewhere is a valid joint probability density function for Y1, the amount of pollutant per sample collected above the stack without the cleaning device, and Y2, the amount collected above the stack with the cleaner. a Find E(Y1) and E(Y2). b Find V(Y1) and V(Y2). c The random variable Y1 Y2 represents the amount by which the weight of pollutant can be reduced by using the cleaning device. Find E(Y1 Y2). d Find V(Y1 Y2). Within what limits would you expect Y1 Y2 to fall?

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STAT-5615: Statistics in Research I Lecture 3 Graphical Procedures & Summary Statistics Ott & Longnecker Chapter 3 Dr. Christian Lucero Virginia Tech Fall 2016 Explaratory Data Analysis (EDA) I EDA is a set of techniques used to explore and summarize data via graphical and numerical methods. I Graphical Techniques (including but not limited to) I Pie charts (not covered in class, please read) I Bar charts I Histograms I Stem-and-Leaf plots (not covered in class, please read) I Time series plots I Boxplots I Numerical Descriptive Techniques I

###### Chapter 5, Problem 5.78 is Solved

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In Exercise 5.10, we proved that f (y1, y2) = $ 1, 0 y1 2, 0 y2 1, 2y2 y1, 0, elsewhere