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Probability Q: one number larger than other

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  • Vamsi Krishna Paruchuri
    Hi friends, Thanks a lot for you guys helping many like me. Anyways I am sort of struggling with the following question: Pick two random numbers between 0 and
    Message 1 of 3 , Dec 1, 2005
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      Hi friends,
      Thanks a lot for you guys helping many like me.

      Anyways I am sort of struggling with the following question:

      Pick two random numbers between 0 and 1: X and Y. I am trying to
      compute the probability of
      X^2 > (Y^2 - c)
      where c is some constant, c < 1.

      Thanks a lot for all your suggestions.

      Vamsi.

      PS: This is not a homework question
    • adh_math
      ... Assuming random means uniformly distributed with respect to Lebesgue measure , you want the area of the region in the unit square [0,1] x [0,1] on which
      Message 2 of 3 , Dec 1, 2005
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        --- In mathforfun@yahoogroups.com, "Vamsi Krishna Paruchuri"
        <vamsi_krishna_p@y...> wrote:
        >
        > Pick two random numbers between 0 and 1: X and Y. I am trying to
        > compute the probability of
        > X^2 > (Y^2 - c)
        > where c is some constant, c < 1.
        >

        Assuming "random" means "uniformly distributed with respect to
        Lebesgue measure", you want the area of the region in the unit
        square [0,1] x [0,1] on which

        Y^2 - X^2 < c.

        This is a routine calculus exercise. :)
      • IcerX Blade
        Integrals anyone? or am i off base ( i haven t gotten to integrals in the teaching myself calculus method of instruction) adh_math
        Message 3 of 3 , Dec 1, 2005
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          Integrals anyone? or am i off base ( i haven't gotten to integrals in the "teaching myself calculus" method of instruction)

          adh_math <no_reply@yahoogroups.com> wrote: --- In mathforfun@yahoogroups.com, "Vamsi Krishna Paruchuri"
          <vamsi_krishna_p@y...> wrote:
          >
          > Pick two random numbers between 0 and 1: X and Y. I am trying to
          > compute the probability of
          > X^2 > (Y^2 - c)
          > where c is some constant, c < 1.
          >

          Assuming "random" means "uniformly distributed with respect to
          Lebesgue measure", you want the area of the region in the unit
          square [0,1] x [0,1] on which

          Y^2 - X^2 < c.

          This is a routine calculus exercise. :)





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