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3) The probability density function for Y is given by 1 L = e = 0, y > 0 0, elsewhere And its cumulative distribution function is given by {1-et, ƒ(y) = ‹ē* P<0< 2.996 0.051 F(y) = a) Use the cumulative distribution method or transformation method to show that is a pivotal quantity. b) Using the pivotal quantity in part a) show that a 90% confidence interval of 0 is given by y> 0 0, elsewhere

3) The probability density function for Y is given by 1 L = e = 0, y > 0 0, elsewhere And its cumulative distribution function is given by {1-et, ƒ(y) = ‹ē* P<0< 2.996 0.051 F(y) = a) Use the cumulative distribution method or transformation method to show that is a pivotal quantity. b) Using the pivotal quantity in part a) show that a 90% confidence interval of 0 is given by y> 0 0, elsewhere

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3) The probability density function for Y is given by 1 y ¹e-₁ f(y) = 7 -e, y> 0 0, elsewhere And its cumulative distribution function is given by 음 -e 0 0, elsewhere P( a) Use the cumulative distribution method or transformation method to show that is a pivotal quantity. b) Using the pivotal quantity in part a) show that a 90% confidence interval of 0 is given by 2.996 << 2 Page F(y) = 0.051 9, y > 0 4) According to Chemical Engineering, an important property of fiber is its water absorbency. The average percent absorbency of 25 randomly selected pieces of cotton fiber was found to be 20 with a standard deviation of 1.5. A random sample of 25 pieces of acetate yielded an average percent of 12 with a standard deviation of 1.25. Is there strong evidence that the population mean percent absorbency is significantly higher for cotton fiber than for acetate? 26°C ENG 16:1 2022/10
Transcribed Image Text:3) The probability density function for Y is given by 1 y ¹e-₁ f(y) = 7 -e, y> 0 0, elsewhere And its cumulative distribution function is given by 음 -e 0 0, elsewhere P( a) Use the cumulative distribution method or transformation method to show that is a pivotal quantity. b) Using the pivotal quantity in part a) show that a 90% confidence interval of 0 is given by 2.996 << 2 Page F(y) = 0.051 9, y > 0 4) According to Chemical Engineering, an important property of fiber is its water absorbency. The average percent absorbency of 25 randomly selected pieces of cotton fiber was found to be 20 with a standard deviation of 1.5. A random sample of 25 pieces of acetate yielded an average percent of 12 with a standard deviation of 1.25. Is there strong evidence that the population mean percent absorbency is significantly higher for cotton fiber than for acetate? 26°C ENG 16:1 2022/10
Expert Solution
Step 1

Given:

In this question, the given details are

The given probability density function for Y is,

f(y)=1θe-yθ, y>00  , elsewhere

And then its cumulative distribution function also given as,

F(y)=1-e-yθ,  y>00  , elsewhere

a) Here, to show that the Yθis a pivotal quantity by use the cumulative distribution method or thee transformation method.

b) By using the pivotal quality in the part a) to show that a 90% confidence interval of θ is given by,

PY2.996<θ<Y0.051

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