SlideShare a Scribd company logo
Problem 4. Consider a continuous random variable X with the density function (called the
exponential density) f ( x ) = e x , x >= 0 . 1. Find and sketch the cdf for x . 2. Find the mean and
variance of X . (Hint: Use integration by parts.) 3. Find P ( 1 <= X <= 2 ) . (1) general CDF
formula: x e x d x = 0 x f ( t ) d t [ e x ] 0 x = ( e x ) ( e 0 ) = e x + 1 = 1 e x

More Related Content

More from chahuckfiru

Problem 2 print(-Problem 2-) Ask the user what town they live in- U.docx
Problem 2 print(-Problem 2-)   Ask the user what town they live in-  U.docxProblem 2 print(-Problem 2-)   Ask the user what town they live in-  U.docx
Problem 2 print(-Problem 2-) Ask the user what town they live in- U.docx
chahuckfiru
 
PROBLEM 2 Determine the probability for this normal distribution probl.docx
PROBLEM 2 Determine the probability for this normal distribution probl.docxPROBLEM 2 Determine the probability for this normal distribution probl.docx
PROBLEM 2 Determine the probability for this normal distribution probl.docx
chahuckfiru
 
Principal Diagnosis- list- describe- and code Secondary diagnosis- lis.docx
Principal Diagnosis- list- describe- and code Secondary diagnosis- lis.docxPrincipal Diagnosis- list- describe- and code Secondary diagnosis- lis.docx
Principal Diagnosis- list- describe- and code Secondary diagnosis- lis.docx
chahuckfiru
 
Principles of Macroeconomics 1-To find the slope of a linear function.docx
Principles of Macroeconomics 1-To find the slope of a linear function.docxPrinciples of Macroeconomics 1-To find the slope of a linear function.docx
Principles of Macroeconomics 1-To find the slope of a linear function.docx
chahuckfiru
 
Primary production required to sustain global fisheries D- Pauly- -& V.docx
Primary production required to sustain global fisheries D- Pauly- -& V.docxPrimary production required to sustain global fisheries D- Pauly- -& V.docx
Primary production required to sustain global fisheries D- Pauly- -& V.docx
chahuckfiru
 
primary site for digestion and absorption bolus moves through this 10.docx
primary site for digestion and absorption bolus moves through this 10.docxprimary site for digestion and absorption bolus moves through this 10.docx
primary site for digestion and absorption bolus moves through this 10.docx
chahuckfiru
 
Presume the trait for dimples is Mendelian and that having dimples is.docx
Presume the trait for dimples is Mendelian and that having dimples is.docxPresume the trait for dimples is Mendelian and that having dimples is.docx
Presume the trait for dimples is Mendelian and that having dimples is.docx
chahuckfiru
 
Prepare the entry to record the conversion on April 1- 2021- (The book.docx
Prepare the entry to record the conversion on April 1- 2021- (The book.docxPrepare the entry to record the conversion on April 1- 2021- (The book.docx
Prepare the entry to record the conversion on April 1- 2021- (The book.docx
chahuckfiru
 
Prepare journal entres to establsh a pelfy cash fund on January 1 and.docx
Prepare journal entres to establsh a pelfy cash fund on January 1 and.docxPrepare journal entres to establsh a pelfy cash fund on January 1 and.docx
Prepare journal entres to establsh a pelfy cash fund on January 1 and.docx
chahuckfiru
 
Prepare a classified balance sheet that includes the correct balance f.docx
Prepare a classified balance sheet that includes the correct balance f.docxPrepare a classified balance sheet that includes the correct balance f.docx
Prepare a classified balance sheet that includes the correct balance f.docx
chahuckfiru
 
Predicted outcome of a disease (literally- -state of before knowledge-.docx
Predicted outcome of a disease (literally- -state of before knowledge-.docxPredicted outcome of a disease (literally- -state of before knowledge-.docx
Predicted outcome of a disease (literally- -state of before knowledge-.docx
chahuckfiru
 
Predict whether the GAL gens (Gal1- Gal7 Gal10 and Gal2) will be produ.docx
Predict whether the GAL gens (Gal1- Gal7 Gal10 and Gal2) will be produ.docxPredict whether the GAL gens (Gal1- Gal7 Gal10 and Gal2) will be produ.docx
Predict whether the GAL gens (Gal1- Gal7 Gal10 and Gal2) will be produ.docx
chahuckfiru
 
Premier Corporation has an ROE of 13-5 percent and a payout ratio of 3.docx
Premier Corporation has an ROE of 13-5 percent and a payout ratio of 3.docxPremier Corporation has an ROE of 13-5 percent and a payout ratio of 3.docx
Premier Corporation has an ROE of 13-5 percent and a payout ratio of 3.docx
chahuckfiru
 
Predicted outcome of a disease (literally- -state of before knowledge- (1).docx
Predicted outcome of a disease (literally- -state of before knowledge- (1).docxPredicted outcome of a disease (literally- -state of before knowledge- (1).docx
Predicted outcome of a disease (literally- -state of before knowledge- (1).docx
chahuckfiru
 
Predict whether -galactosidase will be produced by the following E- co.docx
Predict whether -galactosidase will be produced by the following E- co.docxPredict whether -galactosidase will be produced by the following E- co.docx
Predict whether -galactosidase will be produced by the following E- co.docx
chahuckfiru
 
Poverty is only about money and material possessions True FalseThe UN.docx
Poverty is only about money and material possessions True FalseThe UN.docxPoverty is only about money and material possessions True FalseThe UN.docx
Poverty is only about money and material possessions True FalseThe UN.docx
chahuckfiru
 
Problem 10 print(-Problem 10-) Ask the user for two numbers- a and b.docx
Problem 10 print(-Problem 10-)   Ask the user for two numbers- a and b.docxProblem 10 print(-Problem 10-)   Ask the user for two numbers- a and b.docx
Problem 10 print(-Problem 10-) Ask the user for two numbers- a and b.docx
chahuckfiru
 
Problem 1- Suppose Y and Z have joint density p(z-y)-k(k1)(zy)k2 for 0.docx
Problem 1- Suppose Y and Z have joint density p(z-y)-k(k1)(zy)k2 for 0.docxProblem 1- Suppose Y and Z have joint density p(z-y)-k(k1)(zy)k2 for 0.docx
Problem 1- Suppose Y and Z have joint density p(z-y)-k(k1)(zy)k2 for 0.docx
chahuckfiru
 
Problem 1- What are the icculec with the fnllnwing fiol urec- (1 nnint.docx
Problem 1- What are the icculec with the fnllnwing fiol urec- (1 nnint.docxProblem 1- What are the icculec with the fnllnwing fiol urec- (1 nnint.docx
Problem 1- What are the icculec with the fnllnwing fiol urec- (1 nnint.docx
chahuckfiru
 
Pressure-Volume Loop The graph to the right shows the relationship bet.docx
Pressure-Volume Loop The graph to the right shows the relationship bet.docxPressure-Volume Loop The graph to the right shows the relationship bet.docx
Pressure-Volume Loop The graph to the right shows the relationship bet.docx
chahuckfiru
 

More from chahuckfiru (20)

Problem 2 print(-Problem 2-) Ask the user what town they live in- U.docx
Problem 2 print(-Problem 2-)   Ask the user what town they live in-  U.docxProblem 2 print(-Problem 2-)   Ask the user what town they live in-  U.docx
Problem 2 print(-Problem 2-) Ask the user what town they live in- U.docx
 
PROBLEM 2 Determine the probability for this normal distribution probl.docx
PROBLEM 2 Determine the probability for this normal distribution probl.docxPROBLEM 2 Determine the probability for this normal distribution probl.docx
PROBLEM 2 Determine the probability for this normal distribution probl.docx
 
Principal Diagnosis- list- describe- and code Secondary diagnosis- lis.docx
Principal Diagnosis- list- describe- and code Secondary diagnosis- lis.docxPrincipal Diagnosis- list- describe- and code Secondary diagnosis- lis.docx
Principal Diagnosis- list- describe- and code Secondary diagnosis- lis.docx
 
Principles of Macroeconomics 1-To find the slope of a linear function.docx
Principles of Macroeconomics 1-To find the slope of a linear function.docxPrinciples of Macroeconomics 1-To find the slope of a linear function.docx
Principles of Macroeconomics 1-To find the slope of a linear function.docx
 
Primary production required to sustain global fisheries D- Pauly- -& V.docx
Primary production required to sustain global fisheries D- Pauly- -& V.docxPrimary production required to sustain global fisheries D- Pauly- -& V.docx
Primary production required to sustain global fisheries D- Pauly- -& V.docx
 
primary site for digestion and absorption bolus moves through this 10.docx
primary site for digestion and absorption bolus moves through this 10.docxprimary site for digestion and absorption bolus moves through this 10.docx
primary site for digestion and absorption bolus moves through this 10.docx
 
Presume the trait for dimples is Mendelian and that having dimples is.docx
Presume the trait for dimples is Mendelian and that having dimples is.docxPresume the trait for dimples is Mendelian and that having dimples is.docx
Presume the trait for dimples is Mendelian and that having dimples is.docx
 
Prepare the entry to record the conversion on April 1- 2021- (The book.docx
Prepare the entry to record the conversion on April 1- 2021- (The book.docxPrepare the entry to record the conversion on April 1- 2021- (The book.docx
Prepare the entry to record the conversion on April 1- 2021- (The book.docx
 
Prepare journal entres to establsh a pelfy cash fund on January 1 and.docx
Prepare journal entres to establsh a pelfy cash fund on January 1 and.docxPrepare journal entres to establsh a pelfy cash fund on January 1 and.docx
Prepare journal entres to establsh a pelfy cash fund on January 1 and.docx
 
Prepare a classified balance sheet that includes the correct balance f.docx
Prepare a classified balance sheet that includes the correct balance f.docxPrepare a classified balance sheet that includes the correct balance f.docx
Prepare a classified balance sheet that includes the correct balance f.docx
 
Predicted outcome of a disease (literally- -state of before knowledge-.docx
Predicted outcome of a disease (literally- -state of before knowledge-.docxPredicted outcome of a disease (literally- -state of before knowledge-.docx
Predicted outcome of a disease (literally- -state of before knowledge-.docx
 
Predict whether the GAL gens (Gal1- Gal7 Gal10 and Gal2) will be produ.docx
Predict whether the GAL gens (Gal1- Gal7 Gal10 and Gal2) will be produ.docxPredict whether the GAL gens (Gal1- Gal7 Gal10 and Gal2) will be produ.docx
Predict whether the GAL gens (Gal1- Gal7 Gal10 and Gal2) will be produ.docx
 
Premier Corporation has an ROE of 13-5 percent and a payout ratio of 3.docx
Premier Corporation has an ROE of 13-5 percent and a payout ratio of 3.docxPremier Corporation has an ROE of 13-5 percent and a payout ratio of 3.docx
Premier Corporation has an ROE of 13-5 percent and a payout ratio of 3.docx
 
Predicted outcome of a disease (literally- -state of before knowledge- (1).docx
Predicted outcome of a disease (literally- -state of before knowledge- (1).docxPredicted outcome of a disease (literally- -state of before knowledge- (1).docx
Predicted outcome of a disease (literally- -state of before knowledge- (1).docx
 
Predict whether -galactosidase will be produced by the following E- co.docx
Predict whether -galactosidase will be produced by the following E- co.docxPredict whether -galactosidase will be produced by the following E- co.docx
Predict whether -galactosidase will be produced by the following E- co.docx
 
Poverty is only about money and material possessions True FalseThe UN.docx
Poverty is only about money and material possessions True FalseThe UN.docxPoverty is only about money and material possessions True FalseThe UN.docx
Poverty is only about money and material possessions True FalseThe UN.docx
 
Problem 10 print(-Problem 10-) Ask the user for two numbers- a and b.docx
Problem 10 print(-Problem 10-)   Ask the user for two numbers- a and b.docxProblem 10 print(-Problem 10-)   Ask the user for two numbers- a and b.docx
Problem 10 print(-Problem 10-) Ask the user for two numbers- a and b.docx
 
Problem 1- Suppose Y and Z have joint density p(z-y)-k(k1)(zy)k2 for 0.docx
Problem 1- Suppose Y and Z have joint density p(z-y)-k(k1)(zy)k2 for 0.docxProblem 1- Suppose Y and Z have joint density p(z-y)-k(k1)(zy)k2 for 0.docx
Problem 1- Suppose Y and Z have joint density p(z-y)-k(k1)(zy)k2 for 0.docx
 
Problem 1- What are the icculec with the fnllnwing fiol urec- (1 nnint.docx
Problem 1- What are the icculec with the fnllnwing fiol urec- (1 nnint.docxProblem 1- What are the icculec with the fnllnwing fiol urec- (1 nnint.docx
Problem 1- What are the icculec with the fnllnwing fiol urec- (1 nnint.docx
 
Pressure-Volume Loop The graph to the right shows the relationship bet.docx
Pressure-Volume Loop The graph to the right shows the relationship bet.docxPressure-Volume Loop The graph to the right shows the relationship bet.docx
Pressure-Volume Loop The graph to the right shows the relationship bet.docx
 

Recently uploaded

Juneteenth Freedom Day 2024 David Douglas School District
Juneteenth Freedom Day 2024 David Douglas School DistrictJuneteenth Freedom Day 2024 David Douglas School District
Juneteenth Freedom Day 2024 David Douglas School District
David Douglas School District
 
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
EduSkills OECD
 
Wound healing PPT
Wound healing PPTWound healing PPT
Wound healing PPT
Jyoti Chand
 
CIS 4200-02 Group 1 Final Project Report (1).pdf
CIS 4200-02 Group 1 Final Project Report (1).pdfCIS 4200-02 Group 1 Final Project Report (1).pdf
CIS 4200-02 Group 1 Final Project Report (1).pdf
blueshagoo1
 
SWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptxSWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptx
zuzanka
 
MDP on air pollution of class 8 year 2024-2025
MDP on air pollution of class 8 year 2024-2025MDP on air pollution of class 8 year 2024-2025
MDP on air pollution of class 8 year 2024-2025
khuleseema60
 
Bonku-Babus-Friend by Sathyajith Ray (9)
Bonku-Babus-Friend by Sathyajith Ray  (9)Bonku-Babus-Friend by Sathyajith Ray  (9)
Bonku-Babus-Friend by Sathyajith Ray (9)
nitinpv4ai
 
Accounting for Restricted Grants When and How To Record Properly
Accounting for Restricted Grants  When and How To Record ProperlyAccounting for Restricted Grants  When and How To Record Properly
Accounting for Restricted Grants When and How To Record Properly
TechSoup
 
Simple-Present-Tense xxxxxxxxxxxxxxxxxxx
Simple-Present-Tense xxxxxxxxxxxxxxxxxxxSimple-Present-Tense xxxxxxxxxxxxxxxxxxx
Simple-Present-Tense xxxxxxxxxxxxxxxxxxx
RandolphRadicy
 
How to Setup Default Value for a Field in Odoo 17
How to Setup Default Value for a Field in Odoo 17How to Setup Default Value for a Field in Odoo 17
How to Setup Default Value for a Field in Odoo 17
Celine George
 
Skimbleshanks-The-Railway-Cat by T S Eliot
Skimbleshanks-The-Railway-Cat by T S EliotSkimbleshanks-The-Railway-Cat by T S Eliot
Skimbleshanks-The-Railway-Cat by T S Eliot
nitinpv4ai
 
220711130083 SUBHASHREE RAKSHIT Internet resources for social science
220711130083 SUBHASHREE RAKSHIT  Internet resources for social science220711130083 SUBHASHREE RAKSHIT  Internet resources for social science
220711130083 SUBHASHREE RAKSHIT Internet resources for social science
Kalna College
 
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 8 - CẢ NĂM - FRIENDS PLUS - NĂM HỌC 2023-2024 (B...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 8 - CẢ NĂM - FRIENDS PLUS - NĂM HỌC 2023-2024 (B...BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 8 - CẢ NĂM - FRIENDS PLUS - NĂM HỌC 2023-2024 (B...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 8 - CẢ NĂM - FRIENDS PLUS - NĂM HỌC 2023-2024 (B...
Nguyen Thanh Tu Collection
 
Contiguity Of Various Message Forms - Rupam Chandra.pptx
Contiguity Of Various Message Forms - Rupam Chandra.pptxContiguity Of Various Message Forms - Rupam Chandra.pptx
Contiguity Of Various Message Forms - Rupam Chandra.pptx
Kalna College
 
A Free 200-Page eBook ~ Brain and Mind Exercise.pptx
A Free 200-Page eBook ~ Brain and Mind Exercise.pptxA Free 200-Page eBook ~ Brain and Mind Exercise.pptx
A Free 200-Page eBook ~ Brain and Mind Exercise.pptx
OH TEIK BIN
 
Gender and Mental Health - Counselling and Family Therapy Applications and In...
Gender and Mental Health - Counselling and Family Therapy Applications and In...Gender and Mental Health - Counselling and Family Therapy Applications and In...
Gender and Mental Health - Counselling and Family Therapy Applications and In...
PsychoTech Services
 
Data Structure using C by Dr. K Adisesha .ppsx
Data Structure using C by Dr. K Adisesha .ppsxData Structure using C by Dr. K Adisesha .ppsx
Data Structure using C by Dr. K Adisesha .ppsx
Prof. Dr. K. Adisesha
 
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdfREASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
giancarloi8888
 
Educational Technology in the Health Sciences
Educational Technology in the Health SciencesEducational Technology in the Health Sciences
Educational Technology in the Health Sciences
Iris Thiele Isip-Tan
 
Haunted Houses by H W Longfellow for class 10
Haunted Houses by H W Longfellow for class 10Haunted Houses by H W Longfellow for class 10
Haunted Houses by H W Longfellow for class 10
nitinpv4ai
 

Recently uploaded (20)

Juneteenth Freedom Day 2024 David Douglas School District
Juneteenth Freedom Day 2024 David Douglas School DistrictJuneteenth Freedom Day 2024 David Douglas School District
Juneteenth Freedom Day 2024 David Douglas School District
 
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
 
Wound healing PPT
Wound healing PPTWound healing PPT
Wound healing PPT
 
CIS 4200-02 Group 1 Final Project Report (1).pdf
CIS 4200-02 Group 1 Final Project Report (1).pdfCIS 4200-02 Group 1 Final Project Report (1).pdf
CIS 4200-02 Group 1 Final Project Report (1).pdf
 
SWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptxSWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptx
 
MDP on air pollution of class 8 year 2024-2025
MDP on air pollution of class 8 year 2024-2025MDP on air pollution of class 8 year 2024-2025
MDP on air pollution of class 8 year 2024-2025
 
Bonku-Babus-Friend by Sathyajith Ray (9)
Bonku-Babus-Friend by Sathyajith Ray  (9)Bonku-Babus-Friend by Sathyajith Ray  (9)
Bonku-Babus-Friend by Sathyajith Ray (9)
 
Accounting for Restricted Grants When and How To Record Properly
Accounting for Restricted Grants  When and How To Record ProperlyAccounting for Restricted Grants  When and How To Record Properly
Accounting for Restricted Grants When and How To Record Properly
 
Simple-Present-Tense xxxxxxxxxxxxxxxxxxx
Simple-Present-Tense xxxxxxxxxxxxxxxxxxxSimple-Present-Tense xxxxxxxxxxxxxxxxxxx
Simple-Present-Tense xxxxxxxxxxxxxxxxxxx
 
How to Setup Default Value for a Field in Odoo 17
How to Setup Default Value for a Field in Odoo 17How to Setup Default Value for a Field in Odoo 17
How to Setup Default Value for a Field in Odoo 17
 
Skimbleshanks-The-Railway-Cat by T S Eliot
Skimbleshanks-The-Railway-Cat by T S EliotSkimbleshanks-The-Railway-Cat by T S Eliot
Skimbleshanks-The-Railway-Cat by T S Eliot
 
220711130083 SUBHASHREE RAKSHIT Internet resources for social science
220711130083 SUBHASHREE RAKSHIT  Internet resources for social science220711130083 SUBHASHREE RAKSHIT  Internet resources for social science
220711130083 SUBHASHREE RAKSHIT Internet resources for social science
 
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 8 - CẢ NĂM - FRIENDS PLUS - NĂM HỌC 2023-2024 (B...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 8 - CẢ NĂM - FRIENDS PLUS - NĂM HỌC 2023-2024 (B...BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 8 - CẢ NĂM - FRIENDS PLUS - NĂM HỌC 2023-2024 (B...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 8 - CẢ NĂM - FRIENDS PLUS - NĂM HỌC 2023-2024 (B...
 
Contiguity Of Various Message Forms - Rupam Chandra.pptx
Contiguity Of Various Message Forms - Rupam Chandra.pptxContiguity Of Various Message Forms - Rupam Chandra.pptx
Contiguity Of Various Message Forms - Rupam Chandra.pptx
 
A Free 200-Page eBook ~ Brain and Mind Exercise.pptx
A Free 200-Page eBook ~ Brain and Mind Exercise.pptxA Free 200-Page eBook ~ Brain and Mind Exercise.pptx
A Free 200-Page eBook ~ Brain and Mind Exercise.pptx
 
Gender and Mental Health - Counselling and Family Therapy Applications and In...
Gender and Mental Health - Counselling and Family Therapy Applications and In...Gender and Mental Health - Counselling and Family Therapy Applications and In...
Gender and Mental Health - Counselling and Family Therapy Applications and In...
 
Data Structure using C by Dr. K Adisesha .ppsx
Data Structure using C by Dr. K Adisesha .ppsxData Structure using C by Dr. K Adisesha .ppsx
Data Structure using C by Dr. K Adisesha .ppsx
 
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdfREASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
 
Educational Technology in the Health Sciences
Educational Technology in the Health SciencesEducational Technology in the Health Sciences
Educational Technology in the Health Sciences
 
Haunted Houses by H W Longfellow for class 10
Haunted Houses by H W Longfellow for class 10Haunted Houses by H W Longfellow for class 10
Haunted Houses by H W Longfellow for class 10
 

Problem 4- Consider a continuous random variable X with the density fu.docx

  • 1. Problem 4. Consider a continuous random variable X with the density function (called the exponential density) f ( x ) = e x , x >= 0 . 1. Find and sketch the cdf for x . 2. Find the mean and variance of X . (Hint: Use integration by parts.) 3. Find P ( 1 <= X <= 2 ) . (1) general CDF formula: x e x d x = 0 x f ( t ) d t [ e x ] 0 x = ( e x ) ( e 0 ) = e x + 1 = 1 e x