Normal distribution

  • Thread starter Kinetica
  • Start date
  • #1
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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:

Answers and Replies

  • #2
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What is the definition of ф[(x-m)/σ], write out the left hand side and the right hand side.
 
  • #3
88
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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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