Question

Two​ tire-quality experts examine stacks of tires and assign a quality rating to each tire on a​ 3-point scale. Let X denote the rating given by expert A and Y denote the rating given by expert B. The following table gives the joint distribution for X and Y. Find

mu Subscript Upper XμX

and mu Subscript Upper YμY

Click the icon to view the joint distribution for X and Y.

		y
f left parenthesis x comma y right parenthesisf(x,y)		1	2	3
	1	0.090.09	0.060.06	0.030.03
x	2	0.090.09	0.370.37	0.060.06
	3	0.020.02	0.090.09	0.190.19

Answer 1

	y=1	y=2	y=3	P(X=x) (row total)
x=1	0.09	0.06	0.03	0.18
x=2	0.09	0.37	0.06	0.52
x=3	0.02	0.09	0.19	0.3
P(Y=y) (column total)	0.2	0.52	0.28	1

μX = sum(xP(X=x)) = (1*0.18)+(2*0.52)+(3*0.3) = 2.12

μY = sum(yP(Y=y)) = (1*0.2)+(2*0.52)+(3*0.28) = 2.08