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SGS
05-11-2005, 02:54 PM
Problem 1- An absent minded person puts an exponential(1) amount of air in a balloon. Find the distribution of the radius of the balloon. Volume of a sphere = (4(pie)r^3)/3.

Problem 2- We take a stick of length 1 and break it into 3 pieces. To be precise, we think of taking the unit interval and cutting at X&lt;Y where X and Y have joint density f(x,y)=2 for 0&lt;x&lt;y&lt;1. What is the probability we can make a triange with the 3 pieces? (can do if no piece is longer than 1/2). Thank in advance for any help.

SGS

SGS
05-12-2005, 02:37 PM
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Delphin
05-12-2005, 02:51 PM
Problem 1 - raise all in.

Problem 2 - fold preflop.

carsten
05-14-2005, 04:24 PM
Problem 1 does not look well-defined. If you want help with your homework, at least copy the assignments carefully.

In problem 2, we're given a constant density function, hence the task is simply to find the area of favorable outcomes and divide it by the area of possible outcomes. (Exercise for the reader: Explain why this is so.)

The possible outcomes are the set of (x,y) such that 0&lt;x&lt;y&lt;1. The favorable outcomes are the set of (x,y) such that 0&lt;x&lt;y&lt;1/2. Exercise for the reader: Sketch the corresponding areas to find the answer.

Hope this helps,

Carsten.