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Validity conditions: p_XY(x, y) >= 0 and sum over all (x, y) equals 1 is part of Two Discrete Random Variables, Week 1 in Statistics 2. Prasnya files every IIT Madras BS previous year question from this subtopic here, each one with a worked explanation. Take the whole set as a timed mock and you get accuracy, pacing and per-question analysis back.
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