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Finding distribution function

  1. Oct 2, 2009 #1
    1. The problem statement, all variables and given/known data

    Let X have an Exp(1/2) distribution. Determine the distribution function of 1/2X. What kind of distribution does 1/2X have?


    3. The attempt at a solution

    I can't seem to do this quite properly. I thought of doing the integral from x to -inf of 1/2X dx but that doesn't seem right. I know what a exponential distribution is but nothing else from there.

    Is it just something like X = exp(1/2) therefore 1/2X = exp(1/4) or something along those lines?


    thanks for the help in advance.
     
  2. jcsd
  3. Oct 2, 2009 #2

    LCKurtz

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    Does 1/2X mean (1/2)X or 1/(2X)? I guess I will assume the former. Parentheses do serve a purpose you know.

    If Y = (1/2)X then P(Y ≤ x) = P((1/2)X ≤ x) = P(X ≤ 2x)

    Does that help you?
     
  4. Oct 2, 2009 #3
    im sorry, its (1/2)X.

    Does this change anything?

    also along those same lines, theres another part to the question which is exactly the same as above but its:

    let X have a exp(lambda) distribution.....determine the distribution function of (lambda)X and what kind of distribution does this have?
     
  5. Oct 2, 2009 #4

    LCKurtz

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    "Does this change anything?"

    No, I assumed that.

    "also along those same lines, theres another part to the question which is exactly the same as above but its:

    let X have a exp(lambda) distribution.....determine the distribution function of (lambda)X and what kind of distribution does this have?"

    Did you understand my first reply. That should help.
     
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