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Homework Help: Density function question

  1. Feb 2, 2010 #1
    [tex]Y-U(-2\pi,2\pi)[/tex]
    find the density function of z=tan(Y)
    ?

    i had a similar question

    X-U(0,1)
    find the density function of W=a+bx
    the solution is
    W-U(a,a+b)

    how to solve the first question ??
     
  2. jcsd
  3. Feb 2, 2010 #2

    HallsofIvy

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    Please, tell us what you are talking about!

    I think that you are saying that uniformly distributed between [itex]-2\pi[/itex] and [itex] and [itex]2\pi[/itex], but I have to guess that bcause you didn't even say this was a probability question!

    What have you done? You know that you are to show what efforts you have already made don't you?

    What is the density function for Y?
     
  4. Feb 2, 2010 #3
    it is probability question

    the density function of Y is distributed evenly
    [tex]
    Y-U(-2\pi,2\pi)
    [/tex]

    i tried to solve it like the example question i showed

    but here in tangense i have no idea
    because i could find teh density by this
    (tan(-2pi),tan(2p))
    but this is wrong because if we have an interval mutiplication streches it
    subtraction moves it to the left
    but tangense
    i have no idea
     
  5. Feb 2, 2010 #4

    HallsofIvy

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    Since Y itself is uniformly distributed from [itex]-2\pi[/itex] to [itex]2\pi[/itex], its cumulative probability function is [itex]x/(2\pi)[/itex] an its density function is the constant [itex]dY/dx= 1/(2\pi)[/itex]. The density function of Z= tan(Y) is the derivative of tan(Y): [itex]d(tan(x/(2\pi))[/itex].
     
  6. Feb 2, 2010 #5
    you said facts but how you get to them?
    the final solution is
    [tex]f_z(t)\frac{1}{\pi(1+t^2)}[/tex]
    so its like you said

    but i cant see a logical way like in the solved example i showed
    ?
     
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