Proving Mean and Variance Equivalence: Step-by-Step Guide | Helpful Tips

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SUMMARY

The discussion focuses on proving the equivalence of mean and variance for a transformed random variable Y, defined as Y = aX, where X is a specified distribution. The key formulas used are E[Y] = E[aX] = aE[X] and Var[Y] = Var[aX] = a²Var[X]. Participants emphasize the necessity of defining the original distribution X to accurately compute the mean and variance of Y. The conversation highlights the importance of understanding the relationship between linear transformations and their statistical properties.

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  • Understanding of random variables and distributions
  • Familiarity with the concepts of expected value and variance
  • Knowledge of linear transformations in statistics
  • Basic proficiency in mathematical notation and operations
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Statisticians, data analysts, and students studying probability and statistics who seek to deepen their understanding of the relationships between mean and variance in transformed variables.

mcguiry03
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μ=αθ
σ^2=αθ^2
can someone show me how to prove that the mean and variance is equal to what is at the top... tnx a lot...:biggrin:
 
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Hey mcguiry03 and welcome to the forums.

You need to specify what the distribution is and what you are trying to do.

If you are starting with a distribution X and you have Y =aX and want to find the mean and variance of Y then you use the fact that E[Y] = E[aX] = aE[X] and Var[Y] = Var[aX] = a^2Var[X].

If it is something else, then you will need to specify what is going on and what you are trying to do.
 
tnx sir
 

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