Proof of variance for functions of variable

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SUMMARY

The discussion centers on the proof of Theorem 4.3 related to variance in the context of random variables. Participants reference Definition 4.3 and its application to the random variable Y=g(X) as a key step in understanding the theorem. A critical observation is made regarding a missing squaring of the variance in the provided proof, which hinders comprehension. Clarifying this detail is essential for fully grasping Theorem 4.3 and its implications.

PREREQUISITES
  • Understanding of random variables and their properties
  • Familiarity with variance and its mathematical definitions
  • Knowledge of Theorem 4.3 and its context within probability theory
  • Ability to interpret mathematical proofs and definitions
NEXT STEPS
  • Review the proof of Theorem 4.3 in detail
  • Study the implications of Definition 4.3 on variance calculations
  • Examine the relationship between random variables and their transformations
  • Explore additional resources on variance proofs in probability theory
USEFUL FOR

Students of probability theory, mathematicians focusing on statistical proofs, and educators teaching concepts of variance and random variables.

georg gill
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http://bildr.no/view/1115383

i wonder if anyone could explain the proof for theorem 4.3 i have understood definition 4.3
 
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Hi Georg.
I don't know which is definition 4.1, but it doesn't matter.
If you take definition 4.3 and apply it to the random variable Y=g(X), you'll get it.
 
http://bildr.no/view/1115856

above is definition 4.1. In the first link that they have forgot to square the variance that appears after the text:

"It follows from Definition 4.3 that.." ?

If they would have done that I would have understood the theorem 4.3 and its proof
 

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