# Probability mass function, sampling without replacement

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A bin of 5 transistors is known to contain 2 that are defective. The transistors are to be tested, one at a time, until the defective ones are identified. Denote by N1 the number of tests made until the first defective is identified and by N2 the number of additional tests until the second defective is identified: find the joint probability mass function of N1 and N2. See the attached file.

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In this function we find the joint probability mass function (pmf) of two random variables when sampling from a bin of 5 transistors known to contain 2 that are defective.

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This problem becomes very simple if you list the ways that 2 indistinguishable objects of one type (the defectives) can be distributed among 3 indistinguishable objects of another type (the non-defectives). Among the five potential "locations" where the defectives can show up, two of them must be chosen to define a simple event in the sample space. The ...

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