00:02
Hi there, welcome to number one.
00:04
We are going to cover this question relating to jointly probability density function and density function.
00:14
Okay, so first we have to find the constant c in other to find the constant c then we have to check that the interation in terms of x and y in this case it's just on on meserable space c of e to the negative signal and 9x minus 3y, dx, dx, dy equal to 1.
00:38
So you have to verify this, and you have to do the real work.
00:42
You have to do the computation.
00:44
Here you see x is not given, right? so it's just from negative infinity to positive infinity.
00:53
But you can see here's the relationship when y is between from 0 to x.
00:58
So you have to replace 0 to x and x is from 0 to infinity.
01:02
Right so you can compute d y first and the x later and then you find this iteration then you can find a constant c right because the total density equal to one right so that is the hint for c so after you find the constant c then you can do question a right so question a is saying that the probability that x less than 1 and y less than 10, which means that all the domain that x less than 1 and all the domain that y less than 10, sorry 1 over 10 of the function f of x y the x, sorry the x, and here you you have to, sorry, the y the x, right? you have to do it precisely but basically it's not that hard because we know that x, so the interaction should be from 0 to 1 and y is bigger than 0 and less than 1 over 10, right? so 1 over 10.
02:16
Okay, so here is the tricky part of the...
02:19
So we already have the content c so you just replace that inside and f x y d...
02:24
D, y, d x...