Hi! I'm new here and sure that you guys are able to help me out. I've got stuck with this assignment that I don't know how to solve. My problem is that I don't know what limits I should use for the integrals.
You can see the problem here:
http://img103.imagevenue.com/img.php..._122_916lo.jpg
a) Find P(Y1 < 2, Y2>1)
I found the right answer to this one, but there are also a B- and a C-assignment, which I don't know how to solve.
b) Find P(Y1> or equal to 2Y2)
The correct answer is 1/2.
c) P(Y1-Y2> or equal to 1)
The correct answer in this is e^-y1
Can you please show how to limit the integrals as well?
Thanks a lot!
Thanks a lot! But why can y2 go from 0 - infinity when there is a restriction that y2 must be smaller than or equal to y1? And can you please show how to calculate the B-assignment as well? I don't get it right anyway. Once again, thanks a lot for your help. And you were right about the answer in C, i read it wrong from the book.
Thanks again. I've got two other problems that I've been stuck with for a couple of days. I'd be so glad if someone could help me out with these. Since I'm not very good at writing down the problems, I took a photo of the two assignments that you can see here: http://img121.imagevenue.com/img.php..._122_582lo.jpg
The problem is the same here, I'm not sure how to limit the integrals, and when I start calculate I always go wrong. So I'd be very grateful for a quite detailed explanation. It'd make my day!
New questions should be posted in a new thread.
For (a) and (b) does the notation mean and .
For all three questions you first need to draw on a set of Y1-Y2 axes the region over which you're doing the double integral. Can you show the region represented by and .
(a) and (b) Can you show the appropriate part of the above region?
(c) Can you then show the region corresponding to ?
What experience do you have in setting up and solving double integrals? Doing this looks like your real problem - my advice is that you first learn/consolidate/revise this material before trying these sorts of questions.
Thanks for your help. I've managed to solve a and b. And I'm quite good at solving the integrals, my problem is that I don't always know how to limit them. Now I don't know how to limit the integral to solve P(Y1>Y2) I've drawn a picture of the integration area, which you can see here:
http://img203.imagevenue.com/img.php..._122_494lo.jpg
The red area is where Y1>Y2, but I need some help to limit the integrals. Thanks in advance.
The first thing you need to do is get the coordinates of the intersection point of the lines and . Let them be (a, b). Then one possible double integral is:
.
It's no good being able to integrate if you can't set up the appropriate integrals with the required integral terminals - you obviously have to work on this.