In an automobile plant two tasks are performed by robots The

In an automobile plant, two tasks are performed by robots. The first entails welding two joints, and the second entails tightening three bolts. Let X denote the number of defective welds and Y the number of improperly tightened bolts produced per car. Past data indicates that the joint density for (X, Y) is as shown below and each entry in the table can be interpreted as a probability. Determine (i) the marginal distributions for X and Y, (ii) Cov(X, Y) and (X, Y), and (iii) if X and Y are independent or dependent showing the rationale for your answer.

X/Y 0 1 2 3

0 0.840 0.030 0.020 0.010

1 0.060 0.010 0.008 0.002

2 0.010 0.005 0.004 0.001

Solution