Final answer:
To show that the joint Gaussian PDF fX,Y(x,y) satisfies ∫[infinity][infinity]∫[infinity][infinity]fX,Y(x,y)dxdy=1, we can use Equation (5.68) and the result of Problem 4.6.13.
Step-by-step explanation:
To show that the joint Gaussian PDF fX,Y(x,y) satisfies ∫[infinity][infinity]∫[infinity][infinity]fX,Y(x,y)dxdy=1, we can use Equation (5.68) and the result of Problem 4.6.13. First, let's recall the definition of a continuous probability density function (pdf), which states that the total area under the curve f(x) is one. In this case, we have a joint Gaussian PDF, which describes the probability distribution of two continuous random variables, X and Y, and can be denoted as fX,Y(x,y).
Using the definition of a continuous probability density function, we know that the area under the graph of fX,Y(x,y) and between any values of x and y gives the probability. Therefore, integrating fX,Y(x,y) over the entire range of x and y should give us a probability of one. This can be expressed as ∫[infinity][infinity]∫[infinity][infinity]fX,Y(x,y)dxdy=1.