Anyone know how to solve this question?

deathstar9 · December 3rd, 2008, 3:32 am

There is a 1ft line segment, you pick two pts on the segment uniformly and independently.Find the probability that the distance between the two points is greater then 1/2ft.

wileysw · December 3rd, 2008, 3:48 am

1/4.algebraically, the prob is where x and y are the coordinates where you break the stick.

ehremo · December 3rd, 2008, 6:52 am

We havetherefore choosing A = { (X,Y) : |X-Y| > 0.5 }, the probability is clearly 0.25 (draw yourself a diagram)

deathstar9 · December 3rd, 2008, 10:25 pm

Thanks guys, do any of you know how to get an approximation of this answer using excel?

MCarreira · December 4th, 2008, 1:45 am

QuoteOriginally posted by: deathstar9Thanks guys, do any of you know how to get an approximation of this answer using excel?

deathstar9 · December 4th, 2008, 2:45 am

Thanks again, my AP Stat teacher gave my class this problem for extra credit, of course its practically impossible for us to solve considering AP Stat is not even a calc based course. We are only just starting to learn integration in AP Calculus.

vxs · December 14th, 2008, 8:15 pm

WileyswI had a question... pardon my ignorance... why do you multiply by 2, wouldn't the integrals take care of it the "both sides" aspect of it. My confusion arises from the fact that I am getting 0.125 (1/8) by MC as well.Thanks

katastrofa · December 14th, 2008, 10:11 pm

QuoteOriginally posted by: deathstar9Thanks again, my AP Stat teacher gave my class this problem for extra credit, of course its practically impossible for us to solve considering AP Stat is not even a calc based course. We are only just starting to learn integration in AP Calculus.Of course it is possible to solve it without calculus, you just need to try a little bit harder.Hint: use geometry.

Traden4Alpha · December 14th, 2008, 10:32 pm

QuoteOriginally posted by: katastrofaQuoteOriginally posted by: deathstar9Thanks again, my AP Stat teacher gave my class this problem for extra credit, of course its practically impossible for us to solve considering AP Stat is not even a calc based course. We are only just starting to learn integration in AP Calculus.Of course it is possible to solve it without calculus, you just need to try a little bit harder.Hint: use geometry.Yes. The "pick two pts on the segment uniformly and independently" defines a uniform distribution on a unit square. The difference function defines a diagonal ruling of the square space and the "greater then 1/2ft" leaves us with only two small corners of the square in the upper left and lower right which are triangles with base of 1/2 and height of 1/2. That yields 2 * (1/2 * 1/2)/2 = 1/4.

wileysw · December 14th, 2008, 11:11 pm

vxs, the integral i wrote down assumes x is smaller and y is larger. both x and y are from 0 to 1, so it can be reversed: y<x. by symmetry, the two cases should be same, which gives the factor of 2.(also if you understand the geometrical picture in Traden4Alpha's post, the double integrals only give the area of one triangle)not sure what went wrong with your MC. you might want to take a look at what MCarreira did.

katastrofa · December 15th, 2008, 7:56 pm

My wife is supposed to be wrapping up her PhD thesis right now, so of course she took the opportunity to procrastinate and drew a graphical solution:This is probably what the teacher expected.