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Random process of uniform- graphing and pdf

  1. Nov 28, 2013 #1
    1. The problem statement, all variables and given/known data

    Word for word of the problem:
    Let N (t, a) = At be a random process and A is the uniform continuous distribution (0, 3).

    (i) Sketch N(t, 1) and N(t, 2) as sample functions of t.


    (ii) Find the PDF of N(2, a) = 2A.


    2. Relevant equations
    A pdf is 1/3 for x in [0,3]


    3. The attempt at a solution

    This question is very vague to me. I am not sure where to start.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 28, 2013 #2

    Ray Vickson

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    You have both a and A; which one do you mean?
     
  4. Nov 28, 2013 #3

    haruspex

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    I'm not familiar with this notation and terminology. I think it's saying that at time t you take a random sample x from A and get xt as the value of N. Is that right? I can only suppose that 'a' represents the random sample value, but that is strange notation since it is a function of t. Anyway, that leads to interpreting N(t, 1) as being the function of time you would get if the sample from A is always the value 1.
    Correspondingly, N(2, a) is the r.v. obtained by taking samples from A and doubling them.
    Does that all make sense?
     
  5. Nov 28, 2013 #4

    Ray Vickson

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    My guess would be that this type of "random process" is hardly what we usually mean by that terminology: I guess we first choose a random realization 'a' of the random variable A, then for all time we have N(t,a) = a*t. That amounts to choosing a random slope for a line, but from then on having a deterministic line. Or so, that is what I read into the problem.
     
  6. Nov 28, 2013 #5

    haruspex

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    Yes, I think that comes to the same as what I wrote, but better expressed.
     
  7. Nov 28, 2013 #6
    That makes sense now.
     
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