Solution Found!
A certain raw material is classified as to moisture
Chapter 4, Problem 8E(choose chapter or problem)
A certain raw material is classified as to moisture content \(X\) (in percent) and impurity \(X\) (in percent). Let \(X\) and \(Y\) have the joint pmf given by
(a) Find the marginal pmfs, the means, and the variances.
(b) Find the covariance and the correlation coefficient of \(X\) and \(Y\).
(c) If additional heating is needed with high moisture content and additional filtering with high impurity such that the additional cost is given by the function \(C=2 X+10 Y^{2}\) in dollars, find \(E(C)\).
Questions & Answers
QUESTION:
A certain raw material is classified as to moisture content \(X\) (in percent) and impurity \(X\) (in percent). Let \(X\) and \(Y\) have the joint pmf given by
(a) Find the marginal pmfs, the means, and the variances.
(b) Find the covariance and the correlation coefficient of \(X\) and \(Y\).
(c) If additional heating is needed with high moisture content and additional filtering with high impurity such that the additional cost is given by the function \(C=2 X+10 Y^{2}\) in dollars, find \(E(C)\).
ANSWER:Step 1 of 9
The given joint pmf is
\(\begin{array}{|c|c|c|c|c|c|} \hline Y \downarrow \backslash X \rightarrow & 1 & 2 & 3 & 4 & f_{X}(x) \\ \hline 2 & 0.1 & 0.2 & 0.3 & 0.05 & 0.65 \\ \hline 1 & 0.05 & 0.05 & 0.15 & 0.1 & 0.35 \\ \hline f_{Y}(y) & 0.15 & 0.25 & 0.45 & 0.15 & 1 \\ \hline \end{array}\)