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Cdf to pdf and vise versa

  1. Nov 7, 2009 #1
    cdf to pdf and vise versa
    hi
    i'm looking for help when going from a cdf function:
    F(x) = { 1- e^-αx^β x ≥ 0, α>0, β>0
    { 0 x < 0

    to getting the corresponding pdf

    also i am looking to do the opposite(pdf to cdf)
    for:
    f(x) = { (1 + α)/2 for -1 ≤ x ≤ 1, -1 ≤ α ≤ 1
    { 0 otherwise

    i'm unsure as to how to integrate and differentiate these parts.
    can you help please

    thanks
    michael
     
  2. jcsd
  3. Nov 7, 2009 #2

    whs

    User Avatar

    You don't need to post the same question in multiple places.
     
  4. Nov 7, 2009 #3
    sorry i just noticed it said put homework in the homework section after i had posted it in the first location
     
  5. Nov 7, 2009 #4

    whs

    User Avatar

    As for differentiating, you need to use the chain rule. Integrating that function should be simple since (1 + a)/2 is a constant with respect to X.
     
  6. Nov 7, 2009 #5
    so would the following look ok for the first part?
    f(x) = {e^-αx^β } {αβ [x^(β-1) } x ≥ 0, α>0, β>0

    and for the second part it should look like
    f(x) = { (1 + αx)/2 for -1 ≤ x ≤ 1, -1 ≤ α ≤ 1 to start off. apologies for missing the x as it is crucial. do you think i can still use 1+α as a constant
    then the answer would look like
    ((1 +α)x^2)/4
     
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