im having issues with some of my webworks problems. ive been sitting here for a few hrs trying to do them but since the text is of no help along with my class notes. i dont know where to start on this weeks problems. here are the ones i need help with:
1. X and Y are uniformly distributed over the square 0x10y1. Find the probability that X−Y, the distance between X and Y, is less than 01
2. A man and a woman agree to meet at a cafe about noon. If the man arrives at a time uniformly distributed between 11:30 and 12:10 and if the woman independently arrives at a time uniformly distributed between 11:45 and 12:50, what is the probability that the first to arrive waits no longer than 15 minutes?
3. (this is basically the same exact problem as number 1) Two points are selected randomly on a line of length 28 so as to be on opposite sides of the midpoint of the line. In other words, the two points X and Y are independent random variables such that X is uniformly distriuted over [014) and Y is uniformly distributed over (1428]. Find the probability that the distance between the two points is greater than 9. answer:
5. Two points along a straight stick of length 31cm are randomly selected. The stick is then broken at those two points. Find the probability that all of the resulting pieces have lenght at least 25cm.
number 5 i really have no idea. number 1 and 3 ive been working on and got solutions but theyre wrong. number 1, 2, and 3 im guessing all have similar approaches but what confuses me is that since there is no function, how do i set up the distribution function to take the intergral or am i missing the approach all togther here
any help would be great!