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    A medical test applied to healthy persons indicates “healthy” with 99% probability. If the same test is applied to a diseased person, it indicates “ill” with 99% probability. We assume that 1% of the patients are diseased. What is the probability that a randomly selected patient is diseased if...
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    Let X and Z be binary random variables with P(X = 1) = p and P(Z = 1) = p. Under which conditions can the distribution of Z + X be (easily) computed, and what are the distribution results? Give mean and variance of X + Z.