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Ex.15 Find the correlation between X (the number of defective welds), and Y (the number of improperly tightened bolts produced per car by assembly line robots)in Ex.1.
Sol. We use the given table to compute E [X2] and E [Y2].
E [X2] = 02 (0.90) + 12 (0.08) + 22 (0.02) = 0.16
E [Y2] = 02 (0.910) + 12 (0.045) + 22 (0.032) + 32 (0.013) = 0.29
In Example 11, we found that E[X] = 0.12 and E[Y] = 0.148. Therefore,
Var X = E [X2] - ( E [X])2 = 0.16 – (0.12) 2 = 0.146
Var Y = E [Y2] - ( E [Y])2 = 0.29 – (0.148) 2 = 0.268
In Example 13, we found that Cov (X,Y) = 0.046. Therefore,
x,y =  =  = 0.23
Since this value does not appear to lie close to 1, we would not expect the observed values of X and Y to exhibit a strong linear trend.
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