cdf and pdf of absolute difference of two standard uniform variables X = |X1 − X2|

[roemi]

Hi guys!

Do you know how to get the cdf and pdf of the absolute difference of two iid standard uniform X1 and X2 : X = |X1 − X2| ?

From wiki (http://en.wikipedia.org/wiki/Triangular_distribution#Distribution_of_the_absolu te_difference_of_two_standard_uniform_variables) we know that the cdf is 2x - x2 and the pdf is 2 -2x.
How do we get it?


Thank you very much!

[bpet]

Hi guys!

Do you know how to get the cdf and pdf of the absolute difference of two iid standard uniform X1 and X2 : X = |X1 − X2| ?


One way is to start with the cdf and work out the probabilities by drawing the region on the unit square.

[roemi]

One way is to start with the cdf and work out the probabilities by drawing the region on the unit square.

Would you give some more hints please... perhaps with the joint pdf/cdf formula ?