Variance and Expected Value Problem

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SUMMARY

The discussion focuses on constructing random variables with specified expected values and variances. Specifically, participants provide examples of random variables where the expected value (E(X)) equals 4 and the variance (VAR(X)) also equals 4. One approach discussed involves creating a random variable A with a mean of 0 and variance of 4, then transforming it to variable B by adding 4, which maintains the desired properties. This method highlights the relationship between transformations of random variables and their statistical properties.

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  • Understanding of random variables and their properties
  • Knowledge of probability mass functions (p.m.f.)
  • Familiarity with expected value and variance calculations
  • Basic concepts of statistical transformations
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Students and professionals in statistics, data science, and mathematics who are looking to deepen their understanding of random variables, expected values, and variances.

dspampi
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Give an example of a random variable (i.e. give the range of values it takes and its p.m.f.) with the following properties: EX = 4, VAR(X)=4. Now give an example of a random variable with a different p.m.f. than the first one you gave, but that still has EX = 4, VAR(X)=4.


So this means then E(X) = E(X^2) - (E(x))^2 right?
I'm not sure if this is the way I should approach the problem?
 
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Not really. They just happen to equal the same number. What I would do is first find a random variable A with a mean of 0 and variance of 4. Then the variable B=A+4 will have a mean of 4 and a variance of 4.
 

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