2015 Series X assignment Q1.14 part ii) a)

Discussion in 'CT3' started by RMehta, Jan 19, 2015.

  1. RMehta

    RMehta Member

    Can someone please get me started on this?

    Struggling to know where to begin with this one, the abs(x) has me perplexed.

    Question (just in case you don't have the notes handy):

    X has a pdf f(x) = 0.5 e(-abs(x)), -inf < x < inf.

    Show that MGF = 1/(1-(t^2)), -1<t<1.

    Thanks!
     
    RMehta, Jan 19, 2015
    #1
  2. C2H6O

    C2H6O Member

    We've to split the function into two parts because

    |x| = x for x > 0 and
    |x| = - x for x < 0

    Rest is just finding the MGF using the definition.
     
    C2H6O, Jan 20, 2015
    #2
  3. John Lee

    John Lee ActEd Tutor Staff Member

    As a slight aside the CT3 examiners asked almost an identical question to this in A14 Q4.
     
    John Lee, Jan 21, 2015
    #3
  4. RMehta

    RMehta Member

    Sorted.

    Thanks very much.
     
    RMehta, Jan 21, 2015
    #4

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