Actuarial Outpost Joint pdf of random variables! Help!
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#1
06-14-2018, 11:30 AM
 Mitsu96 Member Non-Actuary Join Date: Jan 2017 Posts: 88
Joint pdf of random variables! Help!

While, I understand how to double integrate the joint pdf. What confuses me is the break down of the lower and upper bounds of X and Y.
As far as I believe, the lower bound of x should be 0 and the upper bound should be y.
And the lower bound for y should be x and the lower should be 1. However, this isn't the case. Can anyone explain to me why?
Thank you so much for your help!

#2
06-14-2018, 11:39 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,625

When you write a double integral, the limits of the outer integral cannot depend on the variable of integration of the inner integral.

So you could make the outer integral covering x from 0 to 1, with the inner integral covering y from x to 1. Or the outer y from 0 to 1 and the inner x from 0 to y. Those give the same result.
#3
06-14-2018, 12:08 PM
 Mitsu96 Member Non-Actuary Join Date: Jan 2017 Posts: 88

Wow....that makes so much sense!

Thank you so much!

 Tags bounds, help!!!, joint density functions, random variables