1. Consider the function -x² + 7.98x – 12.716.a. Normalize it so that it is a PDF on [2.20, 5.78].b. If that is the PDF for a random variable X, what is the probabilitythat X < 4.67?2. Consider the function In x.a. Normalize it so that it is a PDF on [2.80, 6.76].b. Compute the expected value of the PDF on that interval.c. Compute the variance of the PDF on that same interval.3. Consider the function e-x/116.0.a. Normalize it so that it is a PDF on [0, 0).b. Compute the formula for xa.c. What is the VAR when a =0.95?d. What is the ETL for that same a?

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Answered: 1. Consider the function -a2 + 7.98x –…

1. Consider the function -a2 + 7.98x – 12.716. a. Normalize it so that it is a PDF on [2.20, 5.78]. b. If that is the PDF for a random variable X, what is the probability that X < 4.67?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...

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Question

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1. Consider the function -x² + 7.98x – 12.716.
a. Normalize it so that it is a PDF on [2.20, 5.78].
b. If that is the PDF for a random variable X, what is the probability
that X < 4.67?
2. Consider the function In x.
a. Normalize it so that it is a PDF on [2.80, 6.76].
b. Compute the expected value of the PDF on that interval.
c. Compute the variance of the PDF on that same interval.
3. Consider the function e-x/116.0.
a. Normalize it so that it is a PDF on [0, 0).
b. Compute the formula for xa.
c. What is the VAR when a =
0.95?
d. What is the ETL for that same a?

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