Refer to the Journal of Systems Sciences & Systems Engineering (March 2013) study of the reliability of a manufacturing system for producing integrated circuit (IC) cards that involves two production lines, Exercise 4.6. Recall that items (IC cards) first pass through Line 1, then are processed by Line 2. The probability distribution of the maximum capacity level of each line is reproduced below. Consider an IC card randomly selected at some point in the production process. Let X represent the line number and Y represent the maximum capacity of the line at the time of selection. Assuming the lines operate independently, find the bivariate probability distribution p(x, y).

Data from Exercise 4.6

A team of industrial management university professors investigated the reliability of a manufacturing system that involves multiple production lines (Journal of Systems Sciences & Systems Engineering, March 2013). An example of such a network is a system for producing integrated circuit (IC) cards with  two production lines set up in sequence. Items (IC cards) first pass through Line 1, then are processed by Line 2.The probability distribution of the maximum capacity level Y of each line is shown in the next table. Assume the lines operate independently.

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Line, X Maximum Capacity, Y ply) .01 12 .02 24 .02 36 .95 .002 35 .002 70 .996