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Let X be a random variable with mean μ and variance σ^2. Define Y=(X-μ)/σ. What is...

Let X be a random variable with mean μ and variance σ^2. Define Y=(X-μ)/σ. What is the variance of Y?
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Answer #1

Note: Here we transformed the variable X into Y, shifting origin by μ and dividing a scale factor by σ.

  1. Variance is independent of the change of origin but not of scale i.e. V(X+a)= V(X) and V(aX)= X
  2. The variance of the constant term is zero. So, V(μ)=0.
  3. Since X is a variable and μ is a constant. So, cov(X,μ)=0
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