00:01
So we're told that x and y have a discrete joint distribution and the joint pdf is defined in the following way.
00:09
F of xy is equal to c times the absolute value of x plus y.
00:14
And this is for x's.
00:16
So these are the x values negative 2, negative 1, 0, 1, 2.
00:19
And then y is also defined for negative 2, negative 1, 0, and 2.
00:24
And it's 0 otherwise.
00:29
And something came through the prompt that says f of y.
00:32
Y equals y, which wouldn't work.
00:42
Because if you put in negative 2 for y, it would be negative 2, but you can't have that as a probably, that's impossible to have a probability of negative 2.
00:48
It doesn't work.
00:49
So we're going to look at this and it's zero otherwise.
00:54
And so what we're going to do is going to take out this constant factor 6.
00:57
This is the first we're going to find.
00:58
What's this constant c? so the first thing we're going to do is what we have here is you take the absolute value of the sum.
01:03
So negative 2 plus negative 2 is negative 4, but you take the absolute value is 4.
01:07
Negative 2 plus negative 1 is negative 3.
01:09
Absolute value is positive 3.
01:11
And that, so anyway, that's what we gave here, this table.
01:14
And you'll notice when 2, negative 2 goes to 0, 1, negative 1, 0, 0, 0, 0, negative 2 and 2 0.
01:22
So my point is you're kind of see some patterns here.
01:24
So here's this diagonal of zeros, 4 on these ends here.
01:29
So there's that.
01:30
And then if we sum all these together, we get 40, but the whole distribution should give us 1.
01:37
If we add up all the different combinations, everything, all the probabilities should sum to 1.
01:41
But this is 40.
01:43
And so that means we take all these values and divide them by 40.
01:48
So our distribution is then this.
01:53
So this is the distribution.
01:58
So what i've done is we've taken 4 divided by 40, you get 0 .1.
02:04
3 divided by 40, you get 0 .075.
02:08
2 divided by 40, you get 0 .075.
02:10
And so.
02:10
So on and so forth.
02:11
So this is your distribution.
02:14
So the value of c here, let's be very clear, so the value of c is 1 .40th.
02:22
Now we want to find, and this is for part a.
02:25
Now, part b, we want to find the probability of x equaling 0 and y is negative 2.
02:33
And that we can look at our table...