In a plastic molding operation, each part is classified as to whether it conform

Question

In a plastic molding operation, each part is classified as to whether it conforms to color and length specifications. Define the random variables X and Y as x = {1 if the part conforms to color specifications 0 otherwise y = {1 if the part conforms to length specifications 0 otherwise Assume the joint probability distribution of X and Y is defined by f_xy (x, y). shown in the figure. The marginal probability distributions of X and y are also shown in the figure. The conditional probability mass function f_y|x = f_y(y) is shown in figure b. What is the correlation coefficient for the joint probability distribution? Select one 0.01 0 0.20 0.42 0.32

Explanation / Answer

here E(X) =0.99

and E(Y)= 0.98

E(XY)=0.9702

SD(X) =(0.99-0.992)1/2 =0.0995

and SD(Y) =(0.98-0.982)1/2 =0.14

covariance(X,Y) =E(XY)-E(X)E(Y) =0

hence Correlation =Covar(X,Y)/(SD(X)*SD(Y)) =0

option b

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