2 problems strugglin with

[SGS]

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<Y where X and Y have joint density f(x,y)=2 for 0<x<y<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]

.

[Delphin]

Problem 1 - raise all in.

Problem 2 - fold preflop.

[carsten]

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

Hope this helps,

Carsten.