# A Quick Multiple choice for marginal density function

1. Dec 11, 2013

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

2. Dec 11, 2013

### haruspex

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

3. Dec 11, 2013