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Random Variableshard
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A manufacturing firm produces microchips where the defect rate follows a Poisson process with an average of λ\lambdaλ defects per wafer. If the number of defects XXX per wafer is observed and we introduce a quality control mechanism that replaces a fraction ppp of defective chips with non-defective ones, resulting in a new random variable YYY. How does the variance of YYY compare to the variance of XXX?