This discussion is now closed.
Check out other Related discussions
- 3rd year 2nd semester
- Opinions on the best option modules
- Why are we designed to suffer?
- Academic Breach of Integrity because of AI
- Have a properly functioning ignore list and add the ability to mute forums
- AQA Media studies essay structures
- what Integration technique should I be using?
- AQA A Level Philosophy Paper 1 7172/1 - 19 May 2022 [Exam Chat]
- Suggestion: Thread replies on one page or reply search feature
- Entry for Uni for 2024
- Images of functions
- Hi! I'm new here
- Have a list on what is planned on being imported to react from ST2
- I need to get myself sorted at 27
- DNA replication / Transcription wording
- Clinical scientist vs biomedical scientist
- PDEs diffusion eq question
- opinions on the Myer-briggs (MBTI) personality test
- Knowing which particular integral to use for ordinary differential equations
- How do I know if Maths is right for me at uni?
moment generating functions
By using the moment generating function of the normal distribution, show that if X~N(u,p^2) then aX+b~N(au+b,(a^2)(p^2))
i have used p to denote sigma.
and help appreciated x
i have used p to denote sigma.
and help appreciated x
anyone 
The moment generating function of X ~ N(u, p2) is MX(t) = exp(tu+t2p2/2). So if we define a new random variable Y = aX+b, we have
MY(t) = E(et(aX+b)) = etbMX(ta) = exp(t(au+b) + t2(ap)2/2)
And now by comparison with MX(t), the moment generating function for a standard N(u,p2) variable, we see that Y ~ N(au+b, a2p2).
MY(t) = E(et(aX+b)) = etbMX(ta) = exp(t(au+b) + t2(ap)2/2)
And now by comparison with MX(t), the moment generating function for a standard N(u,p2) variable, we see that Y ~ N(au+b, a2p2).
Related discussions
- 3rd year 2nd semester
- Opinions on the best option modules
- Why are we designed to suffer?
- Academic Breach of Integrity because of AI
- Have a properly functioning ignore list and add the ability to mute forums
- AQA Media studies essay structures
- what Integration technique should I be using?
- AQA A Level Philosophy Paper 1 7172/1 - 19 May 2022 [Exam Chat]
- Suggestion: Thread replies on one page or reply search feature
- Entry for Uni for 2024
- Images of functions
- Hi! I'm new here
- Have a list on what is planned on being imported to react from ST2
- I need to get myself sorted at 27
- DNA replication / Transcription wording
- Clinical scientist vs biomedical scientist
- PDEs diffusion eq question
- opinions on the Myer-briggs (MBTI) personality test
- Knowing which particular integral to use for ordinary differential equations
- How do I know if Maths is right for me at uni?
Latest
Trending
Last reply 3 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
Trending
Last reply 3 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
