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Math Help - F distribution

  1. #1
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    F distribution

    How can you show that the f distribution goes to zero as x approaches infinity
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  2. #2
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    Quote Originally Posted by wantanswers View Post
    How can you show that the f distribution goes to zero as x approaches infinity
    If it didn't then the area under the curve could never equal 1 (or any other finite number for that matter).

    Where are you having trouble in using the pdf to establish this result?
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    show that the limit is zero
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    Quote Originally Posted by wantanswers View Post
    show that the limit is zero
    Yes, I realise what you want to do. What I'm asking is where are you stuck in using the pdf to do this?
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    Sketch the graph of the F density function given in Exercise 1. In particular, show that
    1. f(x) at first increases and then decreases, reaching a maximum at the mode
      x
      = (m - 2)/(m(n + 2)).
    2. f(t) converges to 0 as t approaches infinity.
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  6. #6
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    Quote Originally Posted by wantanswers View Post
    Sketch the graph of the F density function given in Exercise 1. In particular, show that
    1. f(x) at first increases and then decreases, reaching a maximum at the mode
      x = (m - 2)/(m(n + 2)).
    2. f(t) converges to 0 as t approaches infinity.
    The pdf has the form f(x) = C \, \frac{x^{\frac{n}{2} - 1}}{(M + nx)^{\frac{n+m}{2}}} where C is a constant.

    1. Solve f'(x) = 0. I suggest using the quotient rule to get the derivative.

    2. I suggest you first substitute some concrete values for m and n and then attempt taking the limit. This will let you get the feel of things.
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