## Probability Q: one number larger than other

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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
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
• ... 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. :)
• 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)

<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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