SlideShare a Scribd company logo
Find an example of a discrete random variable X having the following property:
Let X1 and X2 be independent and identical to X. Then Z = |X1 X2| is also identical to X.
Solution
Let X1 and X2 iid Bernoullie (0.5) trials, P(X1=0) = P(X1=1) = P(X2=0) = P(X2=1) = 0.5
Now, P(Z=0) = P(X1=X2) = P(X1=X2=0) + P(X1=X2=1) = (0.25*0.25)+(0.25*0.25) = 0.5
And P(Z=1) = 1 - P(Z=0 ) = 1-0.5 = 0.5 (because Z can only take value 0 or 1.
Therefore Z is identical to X

More Related Content

More from solimankellymattwe60

The mitochondrial electron transport system (METS) and the photos.pdf
The mitochondrial electron transport system (METS) and the photos.pdfThe mitochondrial electron transport system (METS) and the photos.pdf
The mitochondrial electron transport system (METS) and the photos.pdf
solimankellymattwe60
 
The disclosure of a contingent liability in the footnotes and on t.pdf
The disclosure of a contingent liability in the footnotes and on t.pdfThe disclosure of a contingent liability in the footnotes and on t.pdf
The disclosure of a contingent liability in the footnotes and on t.pdf
solimankellymattwe60
 
The application architeture is design by the application developer a.pdf
The application architeture is design by the application developer a.pdfThe application architeture is design by the application developer a.pdf
The application architeture is design by the application developer a.pdf
solimankellymattwe60
 
Suppose a company’s ROE is 16. This company’s payout ratio is 40. .pdf
Suppose a company’s ROE is 16. This company’s payout ratio is 40. .pdfSuppose a company’s ROE is 16. This company’s payout ratio is 40. .pdf
Suppose a company’s ROE is 16. This company’s payout ratio is 40. .pdf
solimankellymattwe60
 
Some historians have referred to many of the self-proclaimed “Darwin.pdf
Some historians have referred to many of the self-proclaimed “Darwin.pdfSome historians have referred to many of the self-proclaimed “Darwin.pdf
Some historians have referred to many of the self-proclaimed “Darwin.pdf
solimankellymattwe60
 
Please research Meaningful Use. Prepare a brief report on its origin.pdf
Please research Meaningful Use. Prepare a brief report on its origin.pdfPlease research Meaningful Use. Prepare a brief report on its origin.pdf
Please research Meaningful Use. Prepare a brief report on its origin.pdf
solimankellymattwe60
 
Mention the major difference in the physical phenomena occurring rel.pdf
Mention the major difference in the physical phenomena occurring rel.pdfMention the major difference in the physical phenomena occurring rel.pdf
Mention the major difference in the physical phenomena occurring rel.pdf
solimankellymattwe60
 
My code is not matching up with the results.The output for the cod.pdf
My code is not matching up with the results.The output for the cod.pdfMy code is not matching up with the results.The output for the cod.pdf
My code is not matching up with the results.The output for the cod.pdf
solimankellymattwe60
 
Logical FallociesP1 All college students have pet monkeys.P2 J.pdf
Logical FallociesP1 All college students have pet monkeys.P2 J.pdfLogical FallociesP1 All college students have pet monkeys.P2 J.pdf
Logical FallociesP1 All college students have pet monkeys.P2 J.pdf
solimankellymattwe60
 
IP Security One problem with Internet protocol (IP) is that it has.pdf
IP Security One problem with Internet protocol (IP) is that it has.pdfIP Security One problem with Internet protocol (IP) is that it has.pdf
IP Security One problem with Internet protocol (IP) is that it has.pdf
solimankellymattwe60
 
Genmo CorporationOn the night of February 27, 2012, certain recor.pdf
Genmo CorporationOn the night of February 27, 2012, certain recor.pdfGenmo CorporationOn the night of February 27, 2012, certain recor.pdf
Genmo CorporationOn the night of February 27, 2012, certain recor.pdf
solimankellymattwe60
 
In the formula for determining a populations genotype frequencies, .pdf
In the formula for determining a populations genotype frequencies, .pdfIn the formula for determining a populations genotype frequencies, .pdf
In the formula for determining a populations genotype frequencies, .pdf
solimankellymattwe60
 
How is a cell membrane selectively permeable - what permeates and.pdf
How is a cell membrane selectively permeable - what permeates and.pdfHow is a cell membrane selectively permeable - what permeates and.pdf
How is a cell membrane selectively permeable - what permeates and.pdf
solimankellymattwe60
 
How does apoptosis contribute to development of an organismSolu.pdf
How does apoptosis contribute to development of an organismSolu.pdfHow does apoptosis contribute to development of an organismSolu.pdf
How does apoptosis contribute to development of an organismSolu.pdf
solimankellymattwe60
 
How are mobilehandheld browsers different from the traditional desk.pdf
How are mobilehandheld browsers different from the traditional desk.pdfHow are mobilehandheld browsers different from the traditional desk.pdf
How are mobilehandheld browsers different from the traditional desk.pdf
solimankellymattwe60
 
Explain what might be the result if the kinetochore microtubules file.pdf
Explain what might be the result if the kinetochore microtubules file.pdfExplain what might be the result if the kinetochore microtubules file.pdf
Explain what might be the result if the kinetochore microtubules file.pdf
solimankellymattwe60
 
Complete answers or none , and please read questionCreate an elem.pdf
Complete answers or none , and please read questionCreate an elem.pdfComplete answers or none , and please read questionCreate an elem.pdf
Complete answers or none , and please read questionCreate an elem.pdf
solimankellymattwe60
 
Do you believe it is possible to have effective overall management i.pdf
Do you believe it is possible to have effective overall management i.pdfDo you believe it is possible to have effective overall management i.pdf
Do you believe it is possible to have effective overall management i.pdf
solimankellymattwe60
 
Describe WMANs, the technologies used to implement them, and where t.pdf
Describe WMANs, the technologies used to implement them, and where t.pdfDescribe WMANs, the technologies used to implement them, and where t.pdf
Describe WMANs, the technologies used to implement them, and where t.pdf
solimankellymattwe60
 
Discuss the specific properties of the 5 classes of Immunoglobulins .pdf
Discuss the specific properties of the 5 classes of Immunoglobulins .pdfDiscuss the specific properties of the 5 classes of Immunoglobulins .pdf
Discuss the specific properties of the 5 classes of Immunoglobulins .pdf
solimankellymattwe60
 

More from solimankellymattwe60 (20)

The mitochondrial electron transport system (METS) and the photos.pdf
The mitochondrial electron transport system (METS) and the photos.pdfThe mitochondrial electron transport system (METS) and the photos.pdf
The mitochondrial electron transport system (METS) and the photos.pdf
 
The disclosure of a contingent liability in the footnotes and on t.pdf
The disclosure of a contingent liability in the footnotes and on t.pdfThe disclosure of a contingent liability in the footnotes and on t.pdf
The disclosure of a contingent liability in the footnotes and on t.pdf
 
The application architeture is design by the application developer a.pdf
The application architeture is design by the application developer a.pdfThe application architeture is design by the application developer a.pdf
The application architeture is design by the application developer a.pdf
 
Suppose a company’s ROE is 16. This company’s payout ratio is 40. .pdf
Suppose a company’s ROE is 16. This company’s payout ratio is 40. .pdfSuppose a company’s ROE is 16. This company’s payout ratio is 40. .pdf
Suppose a company’s ROE is 16. This company’s payout ratio is 40. .pdf
 
Some historians have referred to many of the self-proclaimed “Darwin.pdf
Some historians have referred to many of the self-proclaimed “Darwin.pdfSome historians have referred to many of the self-proclaimed “Darwin.pdf
Some historians have referred to many of the self-proclaimed “Darwin.pdf
 
Please research Meaningful Use. Prepare a brief report on its origin.pdf
Please research Meaningful Use. Prepare a brief report on its origin.pdfPlease research Meaningful Use. Prepare a brief report on its origin.pdf
Please research Meaningful Use. Prepare a brief report on its origin.pdf
 
Mention the major difference in the physical phenomena occurring rel.pdf
Mention the major difference in the physical phenomena occurring rel.pdfMention the major difference in the physical phenomena occurring rel.pdf
Mention the major difference in the physical phenomena occurring rel.pdf
 
My code is not matching up with the results.The output for the cod.pdf
My code is not matching up with the results.The output for the cod.pdfMy code is not matching up with the results.The output for the cod.pdf
My code is not matching up with the results.The output for the cod.pdf
 
Logical FallociesP1 All college students have pet monkeys.P2 J.pdf
Logical FallociesP1 All college students have pet monkeys.P2 J.pdfLogical FallociesP1 All college students have pet monkeys.P2 J.pdf
Logical FallociesP1 All college students have pet monkeys.P2 J.pdf
 
IP Security One problem with Internet protocol (IP) is that it has.pdf
IP Security One problem with Internet protocol (IP) is that it has.pdfIP Security One problem with Internet protocol (IP) is that it has.pdf
IP Security One problem with Internet protocol (IP) is that it has.pdf
 
Genmo CorporationOn the night of February 27, 2012, certain recor.pdf
Genmo CorporationOn the night of February 27, 2012, certain recor.pdfGenmo CorporationOn the night of February 27, 2012, certain recor.pdf
Genmo CorporationOn the night of February 27, 2012, certain recor.pdf
 
In the formula for determining a populations genotype frequencies, .pdf
In the formula for determining a populations genotype frequencies, .pdfIn the formula for determining a populations genotype frequencies, .pdf
In the formula for determining a populations genotype frequencies, .pdf
 
How is a cell membrane selectively permeable - what permeates and.pdf
How is a cell membrane selectively permeable - what permeates and.pdfHow is a cell membrane selectively permeable - what permeates and.pdf
How is a cell membrane selectively permeable - what permeates and.pdf
 
How does apoptosis contribute to development of an organismSolu.pdf
How does apoptosis contribute to development of an organismSolu.pdfHow does apoptosis contribute to development of an organismSolu.pdf
How does apoptosis contribute to development of an organismSolu.pdf
 
How are mobilehandheld browsers different from the traditional desk.pdf
How are mobilehandheld browsers different from the traditional desk.pdfHow are mobilehandheld browsers different from the traditional desk.pdf
How are mobilehandheld browsers different from the traditional desk.pdf
 
Explain what might be the result if the kinetochore microtubules file.pdf
Explain what might be the result if the kinetochore microtubules file.pdfExplain what might be the result if the kinetochore microtubules file.pdf
Explain what might be the result if the kinetochore microtubules file.pdf
 
Complete answers or none , and please read questionCreate an elem.pdf
Complete answers or none , and please read questionCreate an elem.pdfComplete answers or none , and please read questionCreate an elem.pdf
Complete answers or none , and please read questionCreate an elem.pdf
 
Do you believe it is possible to have effective overall management i.pdf
Do you believe it is possible to have effective overall management i.pdfDo you believe it is possible to have effective overall management i.pdf
Do you believe it is possible to have effective overall management i.pdf
 
Describe WMANs, the technologies used to implement them, and where t.pdf
Describe WMANs, the technologies used to implement them, and where t.pdfDescribe WMANs, the technologies used to implement them, and where t.pdf
Describe WMANs, the technologies used to implement them, and where t.pdf
 
Discuss the specific properties of the 5 classes of Immunoglobulins .pdf
Discuss the specific properties of the 5 classes of Immunoglobulins .pdfDiscuss the specific properties of the 5 classes of Immunoglobulins .pdf
Discuss the specific properties of the 5 classes of Immunoglobulins .pdf
 

Recently uploaded

How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold MethodHow to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
Celine George
 
Pride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School DistrictPride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School District
David Douglas School District
 
The basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptxThe basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptx
heathfieldcps1
 
writing about opinions about Australia the movie
writing about opinions about Australia the moviewriting about opinions about Australia the movie
writing about opinions about Australia the movie
Nicholas Montgomery
 
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
GeorgeMilliken2
 
Digital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental DesignDigital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental Design
amberjdewit93
 
Smart-Money for SMC traders good time and ICT
Smart-Money for SMC traders good time and ICTSmart-Money for SMC traders good time and ICT
Smart-Money for SMC traders good time and ICT
simonomuemu
 
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Dr. Vinod Kumar Kanvaria
 
BBR 2024 Summer Sessions Interview Training
BBR  2024 Summer Sessions Interview TrainingBBR  2024 Summer Sessions Interview Training
BBR 2024 Summer Sessions Interview Training
Katrina Pritchard
 
S1-Introduction-Biopesticides in ICM.pptx
S1-Introduction-Biopesticides in ICM.pptxS1-Introduction-Biopesticides in ICM.pptx
S1-Introduction-Biopesticides in ICM.pptx
tarandeep35
 
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
IreneSebastianRueco1
 
clinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdfclinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdf
Priyankaranawat4
 
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPLAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
RAHUL
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
adhitya5119
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
PECB
 
Advanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docxAdvanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docx
adhitya5119
 
Liberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdfLiberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdf
WaniBasim
 
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHatAzure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
Scholarhat
 
World environment day ppt For 5 June 2024
World environment day ppt For 5 June 2024World environment day ppt For 5 June 2024
World environment day ppt For 5 June 2024
ak6969907
 
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxChapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Mohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
 

Recently uploaded (20)

How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold MethodHow to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
 
Pride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School DistrictPride Month Slides 2024 David Douglas School District
Pride Month Slides 2024 David Douglas School District
 
The basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptxThe basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptx
 
writing about opinions about Australia the movie
writing about opinions about Australia the moviewriting about opinions about Australia the movie
writing about opinions about Australia the movie
 
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
What is Digital Literacy? A guest blog from Andy McLaughlin, University of Ab...
 
Digital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental DesignDigital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental Design
 
Smart-Money for SMC traders good time and ICT
Smart-Money for SMC traders good time and ICTSmart-Money for SMC traders good time and ICT
Smart-Money for SMC traders good time and ICT
 
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
 
BBR 2024 Summer Sessions Interview Training
BBR  2024 Summer Sessions Interview TrainingBBR  2024 Summer Sessions Interview Training
BBR 2024 Summer Sessions Interview Training
 
S1-Introduction-Biopesticides in ICM.pptx
S1-Introduction-Biopesticides in ICM.pptxS1-Introduction-Biopesticides in ICM.pptx
S1-Introduction-Biopesticides in ICM.pptx
 
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
 
clinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdfclinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdf
 
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPLAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
 
Advanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docxAdvanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docx
 
Liberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdfLiberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdf
 
Azure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHatAzure Interview Questions and Answers PDF By ScholarHat
Azure Interview Questions and Answers PDF By ScholarHat
 
World environment day ppt For 5 June 2024
World environment day ppt For 5 June 2024World environment day ppt For 5 June 2024
World environment day ppt For 5 June 2024
 
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxChapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
 

Find an example of a discrete random variable X having the following.pdf

  • 1. Find an example of a discrete random variable X having the following property: Let X1 and X2 be independent and identical to X. Then Z = |X1 X2| is also identical to X. Solution Let X1 and X2 iid Bernoullie (0.5) trials, P(X1=0) = P(X1=1) = P(X2=0) = P(X2=1) = 0.5 Now, P(Z=0) = P(X1=X2) = P(X1=X2=0) + P(X1=X2=1) = (0.25*0.25)+(0.25*0.25) = 0.5 And P(Z=1) = 1 - P(Z=0 ) = 1-0.5 = 0.5 (because Z can only take value 0 or 1. Therefore Z is identical to X