Thread: rectangular distribution problem

Having another problem. Not sure how to even approach this problem. I figure I should be using rectangular distribution somehow.


Let X and Y denote the lengths of the two sides of a rectangle and let them possess independent rectangular distributions over the interval (0,1).
Calculate the probability that the length of a diagonal of this rectangle will be less than one.


Any help would be appreciated.

Originally Posted by BklynKid

Having another problem. Not sure how to even approach this problem. I figure I should be using rectangular distribution somehow.


Let X and Y denote the lengths of the two sides of a rectangle and let them possess independent rectangular distributions over the interval (0,1).
Calculate the probability that the length of a diagonal of this rectangle will be less than one.


Any help would be appreciated.

The square of the diagonal of the random rectangle is , the probability that the diagonal is less than one is: , which as and , is the probability that a random point in the square lies inside the unit circle.

This probability is equal to the area of the unit circle inside the square, which is a quarter of the area or the unit circle or

RonL

Thanks for the swift reply. To be honest, I don't really understand the reason (I already knew the solution) but perhaps it'll come to me later.

Again, thank you.