 Dear students, let me present to you an example to explain the concept of the support of a continuous random vector. Let us take that situation when we have two random variables, X1 and X2, each of which is of the continuous type. In this case, the support of the probability density function given by small f of X1, X2 is the region of the plane that contains all the points small x1, x2 for which f of x1, x2 is greater than 0. You have for example a room and the room has a floor and the room has walls and of course that has a roof also but for our purpose, just concentrate on the floor and also the axis that is going upward. So the floor, if we call the variables X or Y, then we will simply say the XY floor but if we call it X1, X2, then we can say X1, X2 floor, this plane is the area of this plane which has a surface which is represented by small f of X1, X2 and under the total volume under that surface above that rectangular region or whatever region it is, that total volume has to be equal to 1. So let me come to the simple example, actually as soon as you see a diagram that is now coming up you will find that all of this is actually quite simple. The example is very simple. Let us consider the bivariate uniform distribution rather than any other. The simplest one, the bivariate uniform distribution given by f of X1, X2 is equal to 1 where X1 itself is going from 0 to 1 and X2 also is going from 0 to 1 and f of X1, X2 is equal to 0 elsewhere. Now this distribution that I have shown you, you note that as you can now see in the diagram, it is simply like, we can say like a box, it is like a box with a box in which X1, which is on the axis floor, which is on the X1 axis, our box that is starting from X1 equal to 0 and going up to X1 equal to 1, just concentrate on that particular axis which is being represented by X1. Similarly, if you now concentrate on the other axis which is being represented by X2, you can see that for that also the box, that is starting from X2 equal to 0 and going up to X2 equal to 1. Last but not the least, please note that the height of this box is also equal to 1 because if you concentrate on the vertical axis, that is also up to 1, now when its height is 1, its length is also 1 and its width is also 1, so what is the volume of such a thing, it is the product of the height into the length into the breadth or the width, so 1 into 1 into 1 is equal to 1, so the total volume of this box is equal to 1, so this is how you can understand that whenever you have a bivariate situation where the individual random variables are continuous, you will have a floor and on in some region of that floor on top of that region you will have a surface, which in this particular example is flat, which I am calling a box, actually now I say that it is better not to conceive it like a closed box, but the top that in this case is flat because it is a bivariate uniform distribution, even then it is a surface, because surfaces can be curved, but then you can also have a flat surface, the total volume under the surface in your domain or on the top of the support of your random vector will always be equal to 1.