Compute Variance of Random Variable X

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SUMMARY

The discussion centers on computing the variance of a random variable X using the formula V(X) = E((X - E(X))^2). Participants clarify that the original formula presented incorrectly includes a square root, which actually represents the standard deviation S(X), defined as S(X) = (V(X))^(1/2). The confusion arises from the distinction between variance and standard deviation, emphasizing the need for understanding the linearity of the expectation operator E.

PREREQUISITES
  • Understanding of variance and standard deviation in statistics
  • Familiarity with expectation values in probability theory
  • Basic knowledge of parameter differentiation
  • Ability to interpret mathematical notation and formulas
NEXT STEPS
  • Study the definition and properties of variance and standard deviation in statistics
  • Learn about the linearity of expectation in probability theory
  • Explore parameter differentiation techniques in calculus
  • Review computational formulas for variance, including examples and applications
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Students studying statistics, particularly those tackling probability theory and variance calculations, as well as educators seeking to clarify concepts related to expectation values and their applications.

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Homework Statement



Compute the variance of the random variable X given by

[tex]V(X) = \sqrt{E((X-E(X))^2)}[/tex]
where E(X) is the expectation value of random variable X

Homework Equations



Hint: Use parameter differentiation

The Attempt at a Solution



I have no idea what to do here. I've never taken a class in probability and I have never heard of parameter differentiation. I've seen definitions of variance the same as above minus the square root sign so I'm confused.
 
Last edited:
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http://en.wikipedia.org/wiki/Variance

look at "Computational formula for variance"

hmm you should have no square root; the formula you have is the standard devation S(x)

S(x) = (V(x))^(1/2)

At least what I know of statistics.

Use that E is linear operator (E : expectation value)

But I must say that it is hard so see what is meant by the problem..
 
Last edited:

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