Show that the density function for Y is f ( y ) = { ( 1 Γ ( α ) β α ) y − ( 1 + β ) β ( ln y ) α − 1 , y > 1 0 , elsewhere .

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Answer 1

Question

Chapter 6, Problem 112SE

a.

To determine

Show that the density function for Y is f(y)={(1Γ(α)βα)y−(1+β)β(lny)α−1,y>10, elsewhere.

b.

To determine

Show that E(Y)=(1−β)−α if β<1.

c.

To determine

Show that V(Y)=(1−2β)−α−(1−β)−2α if β<0.5.

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Suppose a sample of O-rings was obtained and the wall thickness (in inches) of each was recorded. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed. Click here to view the table of critical values for normal probability plots. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. 0.191 0.186 0.201 0.2005 0.203 0.210 0.234 0.248 0.260 0.273 0.281 0.290 0.305 0.310 0.308 0.311 Using the correlation coefficient of the normal probability plot, is it reasonable to conclude that the population is normally distributed? Select the correct choice below and fill in the answer boxes within your choice. (Round to three decimal places as needed.) ○ A. Yes. The correlation between the expected z-scores and the observed data, , exceeds the critical value, . Therefore, it is reasonable to conclude that the data come from a normal population. ○…

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Answer 2

Question

Chapter 6, Problem 112SE

a.

To determine

Show that the density function for Y is f(y)={(1Γ(α)βα)y−(1+β)β(lny)α−1,y>10, elsewhere.

b.

To determine

Show that E(Y)=(1−β)−α if β<1.

c.

To determine

Show that V(Y)=(1−2β)−α−(1−β)−2α if β<0.5.

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Answer 3

Question

Chapter 6, Problem 112SE

a.

To determine

Show that the density function for Y is f(y)={(1Γ(α)βα)y−(1+β)β(lny)α−1,y>10, elsewhere.

b.

To determine

Show that E(Y)=(1−β)−α if β<1.

c.

To determine

Show that V(Y)=(1−2β)−α−(1−β)−2α if β<0.5.

Expert Solution & Answer

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Answer 4

Question

Chapter 6, Problem 112SE

a.

To determine

Show that the density function for Y is f(y)={(1Γ(α)βα)y−(1+β)β(lny)α−1,y>10, elsewhere.

b.

To determine

Show that E(Y)=(1−β)−α if β<1.

c.

To determine

Show that V(Y)=(1−2β)−α−(1−β)−2α if β<0.5.

Expert Solution & Answer

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Answer 5

Chapter 6, Problem 112SE

a.

To determine

Show that the density function for Y is f(y)={(1Γ(α)βα)y−(1+β)β(lny)α−1,y>10, elsewhere.

b.

To determine

Show that E(Y)=(1−β)−α if β<1.

c.

To determine

Show that V(Y)=(1−2β)−α−(1−β)−2α if β<0.5.

Answer 6

Chapter 6, Problem 112SE

a.

To determine

Show that the density function for Y is f(y)={(1Γ(α)βα)y−(1+β)β(lny)α−1,y>10, elsewhere.

Answer 7

Chapter 6, Problem 112SE

a.

To determine

Show that the density function for Y is f(y)={(1Γ(α)βα)y−(1+β)β(lny)α−1,y>10, elsewhere.

Answer 8

b.

To determine

Show that E(Y)=(1−β)−α if β<1.

Answer 9

b.

To determine

Show that E(Y)=(1−β)−α if β<1.

Answer 10

c.

To determine

Show that V(Y)=(1−2β)−α−(1−β)−2α if β<0.5.

Answer 11

c.

To determine

Show that V(Y)=(1−2β)−α−(1−β)−2α if β<0.5.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

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Show that the density function for Y is f ( y ) = { ( 1 Γ ( α ) β α ) y − ( 1 + β ) β ( ln y ) α − 1 , y > 1 0 , elsewhere .

Solution Summary: The author explains that the density function for Y is f(y)=

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Show that the density function for Y is f(y)={(1Γ(α)βα)y−(1+β)β(lny)α−1,y>10, elsewhere.

Show that E(Y)=(1−β)−α if β<1.

Show that V(Y)=(1−2β)−α−(1−β)−2α if β<0.5.

Want to see the full answer?

Chapter 6 Solutions

Show that the density function for Y is f ( y ) = { ( 1 Γ ( α ) β α ) y − ( 1 + β ) β ( ln y ) α − 1 , y &gt; 1 0 , elsewhere .

Solution Summary: The author explains that the density function for Y is f(y)=

Concept explainers

Videos

Show that the density function for Y is f(y)={(1Γ(α)βα)y−(1+β)β(lny)α−1,y>10, elsewhere.

Show that E(Y)=(1−β)−α if β<1.

Show that V(Y)=(1−2β)−α−(1−β)−2α if β<0.5.

Want to see the full answer?

Chapter 6 Solutions

Show that the density function for Y is f ( y ) = { ( 1 Γ ( α ) β α ) y − ( 1 + β ) β ( ln y ) α − 1 , y > 1 0 , elsewhere .