Question

Find fY(y) from the domain:

Consider the domain D={(x,y): 0 < x < 1,-x < y < x} and let fix, y)=cx,where c is a constant. 1.1 (4.6 marks) To start with, we wish you to determine c such that f(x, y) a joint density of random vector (X, Y) that takes values on D. order to do that, you must first calculate fix, y) dA where dA is an area element of D, and then deduce c Hence you need to evaluate a double integral, where dA is either dx dy or dy dx (really the same thing, but the ordering implies different orders of integration). In fact, if we write dA the integration can be done in "one piece". So, we will insist that you do the integral as dy dx, then dy dx So your first task is to provide the pairs of limits a b] and [c, d , that determine region D for the order of integration implied by writing dA = dy dx Hint: since the region D is not rectangular, not all of a, b, c, d are constants Notes. 1. Please mark these sub-parts separately and in order. Each of the first two sub-parts uses the list (square bracket) syntax implied by the prompt. 2. Variables c and c are different. Similarly, a and b are used in a generic way below, and are not the same as a and b. The change in typeface is deliberate

Answer 1