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Random variable question

  1. Feb 6, 2010 #1
    If I have random variable, P ~ U(1,2), am I correct in thinking that xP ~ U(1,2) also ? (where x is some constant), or does the range change?

    Thanks.
     
  2. jcsd
  3. Feb 6, 2010 #2

    EnumaElish

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    Since P is U(1, 2), Prob(P < p) = p - 1. Note Prob(P < 1) = 1 - 1 = 0 and Prob(P < 2) = 2 - 1 = 1.

    Assume x > 0, then Prob(xP < p) = Prob(P < p/x) = ...

    Does this help?
     
    Last edited: Feb 6, 2010
  4. Feb 8, 2010 #3
    So Prob(P<p/x) = p/x -1 ?

    when p=x Prob = 0, and 2p = x, Prob = 1

    So xP still follows a Uniform Distribution ~ U(1, 2).

    It looks as though I've assumed this though.
     
  5. Feb 8, 2010 #4
    if U(1,2) is the uniform distribution on (1,2), then the random variable xP would be distributed according to U(x,2x).

    Torquil
     
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