00:01
Welcome to this lesson.
00:03
In this lesson, we will let x and y be continuous random variables with a joint pdf.
00:12
Alright, so we have this in this range.
00:16
So we'll find k so that f of x, y is a joint pdf.
00:22
Okay.
00:24
So to ensure that we have a total probability, the double integral over the double integral over the domain given all right of f of x y the x the y should give us one all right so here we have y from zero to one and x from zero y from zero to one x from zero to y all right of k times x plus y would have d x and y so we'd have to evaluate the inner integral first and for that with respective x would have k times x squared over 2 all right plus k times we can still have the k in there.
01:35
All right, this way.
01:38
You evaluate it from 0 to y, right? and after that, we simply have the dy there.
01:47
So i guess we still have integral from 0 to 1.
01:51
We have, if we put in the other goes to zeros, all right? so this becomes k out.
02:00
This becomes y squared over 2.
02:04
All right.
02:05
Then plus.
02:06
Y squared still the y so we can bring out three over two k all right now we still have integral from zero to one of y squared and this would become three over two k all right multiplying y to the power three over three all right we're evaluating this from zero to so the only non -trivial part is if we put in a one.
02:47
All right.
02:47
So this crosses out that.
02:50
And where that would have.
02:52
So let me say that this should be all equals one.
02:59
It should be close one.
03:01
It should be equals one for total probability.
03:05
And this should be equals one.
03:08
So we'd have k over two.
03:13
All right.
03:14
And here would have...