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Find the p.d.f. and identify.

  1. Jan 23, 2012 #1
    1. The problem statement, all variables and given/known data

    X1 ∼ N(μ112) and X2 ∼ N(μ222)

    Let Y = X1 + X2

    Find the p.d.f. of Y & label the distribution.

    2. Relevant equations



    3. The attempt at a solution

    Not quite sure how to go about this problem.

    µY=E[Y]=E[X1+X2]=E[X1]+E[X2]=µ12

    σY2=E[Y2] - µY2

    E[X12+ 2X1X2 +X22] - (µ12)2

    I think that might be how you start it. Feel free to correct me and start over or continue. Thanks.
     
  2. jcsd
  3. Jan 24, 2012 #2

    vela

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    It's kind of hard to make suggestions without knowing more about what you know. What do you know about sums of random variables?
     
  4. Jan 25, 2012 #3

    Figured it out. The above doesn't account for all moments (rth)

    MX1 + X2 = MX1(t)⋅MX2(t)

    MXi=e[itex]\mu[/itex]it + (1/2)σi2t2

    Following N~([itex]\mu[/itex]1 + [itex]\mu[/itex]2 , σ12 + σ22)
     
    Last edited: Jan 25, 2012
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