(Continuous random variable) Impurities in the batch of the final product of a chemical processoften reflect a serious problem. From a considerable amount of data collected at the plant it isknown that the proportion of impurities (Y) in a batch has a density function given by:= {10(1-y)⁹f(y):0 ≤ y ≤ 1en otro casoThe lot is considered unsaleable, and therefore, is not acceptable if the percentage ofimpurities is higher than 60%.a. Verify that the above function is indeed a probability density function.b. Calculate the probability of rejecting a lot due to impurities.c. Calculate the expected value of impurities in the batch.d. Assume that the lot sells for $792 and you have to pay operating expenses of $50 for the lot.Calculate the expected profit.e. Calculate the standard deviation of the impurities in the lot and the profit.

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Answered: (Continuous random variable) Impurities…

A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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