Quality-control checks on wood paneling involve counting the number of surface f
ID: 2923174 • Letter: Q
Question
Quality-control checks on wood paneling involve counting the number of surface flaws on each panel. On a given 2 x 8 ft panel, let X be the number of surface flaws due to unevein application of the final coat of finishing material, and let Y be the number of surface flaws due to inclusions of foreign particles in the finish. The joint piobability mass function p(x, y) of X and Y is presented in the following table. The marginal probability mass functions are presented as well, in the margins of the table. Find the covariance of X and F. v' 2Pr() 0.05 0.15 0.35 0.05 0.05 0.05 0.20 0.05 0.05 0.25 0.45 P y Cor( X, F) =Explanation / Answer
from above data:
marginal pdf of X:
and marginal pdf of Y:
also E(XY) =0.45
therefore Cov(X,Y)=E(XY)-E(X)(EY) =-0.4125
x P(x) xP(x) x^2P(x) 0 0.3000 0.0000 0.0000 1 0.2500 0.2500 0.2500 2 0.4500 0.9000 1.8000 total 1 1.15 2.05 E(x) = 1.1500