A Quick Multiple choice for marginal density function

[Askhwhelp]

Given a plane with three points, (0,−1), (2,0), and (0,1) with x-axis and y-axis connecting three points to make a triangle. Suppose this triangle represents the support for a joint continuous probability density Pick one of the following:

The marginal density f(y), defined as ∫f(x,y)dx.

i) is an increasing function

ii) is a decreasing function

iii) is neither an increasing or decreasing function

iv) cannot be classified according to its increasing or decreasing character without more
information.

Explain you choice

I pick (iii) when the marginal density function begins at y=-1, it must increase at some point before y=1 since the PDF has to be able to integrate to 1 ..on the other than when it got to y=1 ...it must decrease back to 0...so the marginal density function f(y) could not be increasing or decreasing function right...therefore, the answer would be neither increasing nor decreasing

 

[haruspex]

Suppose this triangle represents the support for a joint continuous probability density

Not sure what that means. Does it mean that the joint density function is uniform over that triangle and zero everywhere else?

 

[Askhwhelp]

Not sure what that means. Does it mean that the joint density function is uniform over that triangle and zero everywhere else?

the triangle is just the support which is the 2D plane (x- and y-axis), we do not know what the joint density behaves