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So, today we discuss We discuss this first and then we will go up to joint characteristic functions. We are given jointly random variable. Then, we define the moment m k r as where p x, y is the joint probability density of x, y x to the power k, y to the power r. And this will be called joint moment of x, y of order n is equal to k plus r. So, it is very much similar to the moment that we dealt with for a single random variable case; it is a generalisation of that to two variables. Certain things follow easily What is m 1, 0; that means x to the power 1, that is, x; y to the power 0, that is, 1; x, p x comma y dx dy. And p x comma y can be written as, that is p x comma y can be written as I mean you can write the entire thing like this. x p x dx; p x comma y will be written like that is, p x comma y is p x times p of y given x. So, this integral is 1; whereas, condition theory x; total probability of y taking values within minus infinity to infinity; that is equal to 1. And t