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Finding Density on U(-1,1)

  1. Feb 5, 2012 #1
    1. The problem statement, all variables and given/known data

    Suppose {Y1,......Yn} are random samples from U(-1,1) distribution. Find the density of V=(2Y1+1)^2

    2. Relevant equations

    Method of transformations for random variables

    3. The attempt at a solution

    I started this problem off by letting X=2Y1+1 because i figured i could find the density of that and then just find the density of V=X^2. I thought i had the problem right but when i went back to the density i got for X=2Y1+1 and integrated it over the interval, it didnt add up to 1. Not sure what i did wrong
     

    Attached Files:

  2. jcsd
  3. Feb 5, 2012 #2

    Ray Vickson

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    Homework Helper

    Be careful about the range of the random variable. As Y1 ranges from -1 to +1, what is the range of 2Y1+1?

    RGV
     
    Last edited: Feb 5, 2012
  4. Feb 5, 2012 #3
    -1 to 3 right?
     
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