Consider the triangle with vertices (0, 0), (1, 0), (0, 1). Suppose that (X, Y ) is a uniformly chosen random point from this triangle. (a) Find the marginal density functions of X and Y . (b) Calculate the expectations E[X] and E[Y ]. (c) Calculate the expectation E[XY ].

The solution is given in attached diagram:

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.