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Homework Help: Statistics PDF and change of variable

  1. Oct 8, 2011 #1
    If the probability density of X is given by

    f(x) =

    {2(1 − x) for 0 ≤ x ≤ 1
    {0 otherwise

    (a) Find the probability density function of Y1 = 2X − 1.

    I do not know how to start this problem can someone please help.
    Is there a formula that Im missing from my notes to solve this problem?
  2. jcsd
  3. Oct 8, 2011 #2


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    Start by finding the cumulative distribution function of Y:

    P(Y ≤ y) = P(2X-1 ≤ y) = P(X ≤ ?)

    Figure that out for various y and use the fact that the density function is the derivative of the distribution function.
  4. Oct 8, 2011 #3
    To add to what LC said:

    If you know the distribution/density of a variable X, what can you say about

    the density/distribution of f(X)?
  5. Oct 8, 2011 #4

    so P(X≤ (Y+1/2))


    that means we can say f(X) gives us the probability of X?
  6. Oct 8, 2011 #5


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    That isn't correct as you have written it. You need proper parentheses and, to be pedantic about it, a lower case y. Then use the density of X to calculate the probability.
  7. Oct 8, 2011 #6
  8. Oct 15, 2011 #7
    can anyone explain the steps towards the solution? i'm really confused here too,thank you
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