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Normal distribution

  1. Jun 4, 2012 #1
    Show that if X is a normally distributed random variable with parameters mu and σ2, then then show that for each real number x we have:

    фX(x)=ф[(x-m)/σ]



    I have really hard time. Any possible hint is greatly appreciated.
     
    Last edited: Jun 4, 2012
  2. jcsd
  3. Jun 4, 2012 #2

    micromass

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    What is the definition of ф[(x-m)/σ], write out the left hand side and the right hand side.
     
  4. Jun 5, 2012 #3
    I know that

    Z= [X-μ]/σ or X=σ Z+μ

    I also know that

    f(x,μ,σ2)=1/ √(2πσ) e -(x-μ)2/(2σ2)=1/σ ф((x-μ)/σ)
     
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