Impurities in batches of product of a chemical process reflect a serious problem. It is known that the proportion of impurities Y in a batch has the following density function. Complete parts (a) through (e) below. f(y)= 9(1-y), 0sy≤ 1, 9 = {901- elsewhere (a) Verify that the given function is a valid density function. Select the correct choice below and, if necessary, fill in the answer boxes within your choice. »$9(1 – y)ºdy: O A. The given function is a valid density function because 9(1 - y) dy = B. The given function is a valid density function because it is at least O everywhere. The given function is a valid density function because it is at least 0 everywhere and because √9(1−y)³ 9(1-y) dy = 1. C. (b) A batch is considered not sellable and then not acceptable if the percentage of impurities exceeds 60%. What is the probability that a batch is considered not acceptable (i.e., Y>0.6)? The probability is (Round to four decimal places as needed.)
Impurities in batches of product of a chemical process reflect a serious problem. It is known that the proportion of impurities Y in a batch has the following density function. Complete parts (a) through (e) below. f(y)= 9(1-y), 0sy≤ 1, 9 = {901- elsewhere (a) Verify that the given function is a valid density function. Select the correct choice below and, if necessary, fill in the answer boxes within your choice. »$9(1 – y)ºdy: O A. The given function is a valid density function because 9(1 - y) dy = B. The given function is a valid density function because it is at least O everywhere. The given function is a valid density function because it is at least 0 everywhere and because √9(1−y)³ 9(1-y) dy = 1. C. (b) A batch is considered not sellable and then not acceptable if the percentage of impurities exceeds 60%. What is the probability that a batch is considered not acceptable (i.e., Y>0.6)? The probability is (Round to four decimal places as needed.)
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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I need help with part b please
Transcribed Image Text:Impurities in batches of product of a chemical process reflect a serious problem. It is known that the proportion
of impurities Y in a batch has the following density function. Complete parts (a) through (e) below.
f(y) = 9(1-y)³, 0sy≤ 1,
9 = {901-
elsewhere
(a) Verify that the given function is a valid density function. Select the correct choice below and, if necessary, fill
in the answer boxes within your choice.
O A. The given function is a valid density function because
B. The given function is a valid density function because it is at least 0 everywhere.
The given function is a valid density function because it is at least 0 everywhere and because
19(1−y)³
9(1-y) dy = 1.
C.
19(1-y)ºdy=\
9(1-y) dy =
(b) A batch is considered not sellable and then not acceptable if the percentage of impurities exceeds 60%.
What is the probability that a batch is considered not acceptable (i.e., Y>0.6)?
The probability is
(Round to four decimal places as needed.)
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