what's the probability a 1 meter steel broke into 3 pieces that forms a triangle

Printable View

- May 15th 2009, 10:21 PMcamilla_xuprobability question
what's the probability a 1 meter steel broke into 3 pieces that forms a triangle

- May 15th 2009, 10:29 PMmatheagle
The 1 meter length is unimportant.

I assume we're making two cuts uniformly distributed along the bar.

So let $\displaystyle X_1$ and $\displaystyle X_2$ be iid U(0,1) rvs.

I checked the three case and each case we want the largest cut to be less than .5.

The cuts are $\displaystyle X_1$, $\displaystyle X_2-X_1$ and $\displaystyle 1-X_2$,

BUT here I'm assuming $\displaystyle X_2>X_1$ which is really the order stats.

I'm trying to figure the logic here.

We need $\displaystyle P(max\{X_1,X_2-X_1,1-X_2\}<.5)$

The joint density of these two is $\displaystyle f(x_1,x_2)=2I(0<x_1<x_2<1)$ - May 15th 2009, 10:34 PMcamilla_xu
is that means Pr(one piece<0.5)=1/2 and the other two we regard them as a whole

umm.. do u mean it's 1/4? - May 16th 2009, 02:42 AMmr fantastic
It will depend on how the stick is broken.

Read the attachment and these:

Stick Broken Into Three Pieces. Solution in Trilinear Coordinates from Interactive Mathematics Miscellany and Puzzles

Random Triangles

Problem 8: Random Triangles and an Introduction to Density

Mathematical Recreations and Essays - Google Book Search - May 16th 2009, 06:36 AMmatheagle
Thanks, I was googling Buffon at 2 :30 am but couldn't find this.