(Continuous random variable) Impurities in the batch of the final product of a chemical process often reflect a serious problem. From a considerable amount of data collected at the plant it is known that the proportion of impurities (Y) in a batch has a density function given by: f(y) = {10(1- -{10(1-y)⁹ 0≤y≤1 en otro caso The lot is considered unsaleable, and therefore, is not acceptable if the percentage of impurities 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.
(Continuous random variable) Impurities in the batch of the final product of a chemical process often reflect a serious problem. From a considerable amount of data collected at the plant it is known that the proportion of impurities (Y) in a batch has a density function given by: f(y) = {10(1- -{10(1-y)⁹ 0≤y≤1 en otro caso The lot is considered unsaleable, and therefore, is not acceptable if the percentage of impurities 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.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
100%
Transcribed Image Text:(Continuous random variable) Impurities in the batch of the final product of a chemical process
often reflect a serious problem. From a considerable amount of data collected at the plant it is
known that the proportion of impurities (Y) in a batch has a density function given by:
= {10(1-y)⁹
f(y):
0 ≤ y ≤ 1
en otro caso
The lot is considered unsaleable, and therefore, is not acceptable if the percentage of
impurities 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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: State give information
VIEWStep 2: Verify that the function is a PDF
VIEWStep 3: Calculate probability of rejecting a lot
VIEWStep 4: Obtain the expected value of impurities
VIEWStep 5: Calculated Expected Profit
VIEWStep 6: Compute standard deviation of the impurities
VIEWStep 7: Find the standard deviation of profit
VIEWSolution
VIEW
Step by step
Solved in 8 steps with 7 images
Similar questions
- Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON