Question

X and Y have joint density function f(x,y)= 2e^−(x+y) for 0≤x≤y<[infinity], f(x,y)=0 otherwise.

(a)Draw the region of support. This is a two-dimensional graph of the plane with the region where f(x,y)>0 shaded.

Answer 1

The region of support for the joint density function is a shaded triangle in the xy-plane, with the base along the line y=x and extending to infinity in the positive y-axis direction.

Step-by-step explanation:

To determine the region of support for the joint density function f(x,y) = 2e^(-x-y), we need to find the values of x and y for which f(x,y) > 0. In this case, since the function is defined as 0≤x≤y<∞, the region of support is the area where x is greater than or equal to 0, y is greater than x, and y extends to infinity.

This can be illustrated as a shaded triangle in the xy-plane, with the base along the line y=x and extending to infinity in the positive y-axis direction.