An electronics company tests for the performance quality of its products by performing nondestructive thermal and magnetic-field tests. The products are classified as adequate (A), not adequate (NA), and partially adequate (PA). A sample of 100 produced the following results:

Determine the joint probability mass function PXY(x,y) and the marginal probability mass functions PX(x) and PY(y). Are the random variables statistically uncorrelated? Why?

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A X = Thermal Test NA PA A 60 80 Y = Magnetic NA Field PA 4 44 222 2 0 24 4