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Math Help - Finding pdfs related to the standard normal

  1. #1
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    Finding pdfs related to the standard normal

    Given a random variable Z is standard normal. I am trying to find the pdfs for the abs(Z) and Z^2.

    I thought to start the abs(Z) by splitting the CDF of Z into two separate integrals and adding them (One for when Z>0 and one for when Z<0). Then I would take the derivative to get back to a pdf, but i am struggling to choose the limits of integration.
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  2. #2
    MHF Contributor matheagle's Avatar
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    I just did the absolute value two days ago on this site.
    see http://www.mathhelpforum.com/math-he...-function.html
    the square can be found in many places, including in older threads at this forum
    but the technique is very similar to the absolute value problem
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  3. #3
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    Thank you. So for the absolute value of a random variable with a standard normal pdf, I got twice the standard normal pdf. And for the squared version I ended with 1/sqrt(2pix)*exp((-1/2)x).
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  4. #4
    MHF Contributor matheagle's Avatar
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    what's pix?
    pi times x?
    ALSO, note that the domain in both case are zero to infinity.
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  5. #5
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    Yes it's pi times x. Sorry, as an aside, a link to software to help write math notation would be helpful as well. I'm not sure I see how the domain helps.
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  6. #6
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by jass10816 View Post
    Yes it's pi times x. Sorry, as an aside, a link to software to help write math notation would be helpful as well. I'm not sure I see how the domain helps.
    hit the QUOTE link, from that you can see how people type the math in TeX.
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