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Math Help - Standardizing A Random Variable

  1. #1
    May 2011

    Standardizing A Random Variable


    To standardize a random variable that is normally distributed, it makes absolute sense to subtract the expected value, \mu, from each value that the random variable can assume--it shifts all of the values such that the expected value is centered at the origin. But how does dividing by the standard deviation play a role in the standardization of a random variable? That part is not as intuitive to me as is subtracting \mu.
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  2. #2
    Junior Member
    Feb 2011

    Re: Standardizing A Random Variable

    I am not sure if I got your question right.

    A standard normally distributed random variable has variance 1.

    Let us consider a r.v. Y with variance \sigma^2 and mean \mu.

    The r.v. \frac{1}{\sigma}( Y-\mu) is now standard normally distributed (since the expectation is linear). In order to get a variance of 1 we therefore have to divide by the standard deviation
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