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Probability Question Help

clutchmfe

Joined
9/13/11
Messages
5
Points
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I'm working on a probability interview question that I found from some website. I'm having some problems.

A point is uniformly distribute on a disk with radius 1.
That is, the density is f(x,y) = C, where 0 <= x^2 + y^2 <= 1.

What is the probability that the distance from the origin is less than x, where 0 <= x <= 1?

From reading this question, it seems like for any given point (x,y) on the disk, I have to determine the probability that the distance of (x,y) from the origin is less than x.

Any help is appreciated? I'm looking for help on the thought process to arrive at the answer.
 
Actually, the question might be mis-phrased.

In any case, I realized it's not nearly as complicated as polar coordinates. All you need to do is look up and visualize the probability integral.
 
the distribution is uniform, so you don't even need to do integration, just simple division/multiplication is enough
 
I think I got the solution.

Probability (Distance is < x) implies the portion of the area of circle covered by x = Pi x^2/ Pi r^2 = x^2

Can someone confirm?
 
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