# Determining Marginal Density Functions

I am given

$$f(x,y) = \begin{cases} 1 & \mathrm{where~}0 \le x \le 1\mathrm{~and~} \max(0,x-1) \le y \le \min(0,x) \\ 0 & \mathrm{otherwise} \end{cases}$$

and asked to find the marginal density functions as well as the joint and marginal distribution function.

I understand that the marginal densities can be found by integrating $f(x,y)$ wrt the opposite variables, however I am unsure the limits of integration.

$f_x(x)$ would be integrated from $0$ to $x$, correct?

what would $y$ be integrated from?

Any help would be greatly appreciated

• Hint: if $x$ is some number in the interval $[0,1]$, say $0.4$, what is $\max(0,x-1)$? What is is $\min(0,x)$? What does that tell you about the valueS of $y$ where $f(0.4,y)$ equals $1$? How does the answer change if $x$ were chosen to be $0.1$? $0.98$? Are you absolutely sure you have copied the problem correctly? – Dilip Sarwate Feb 6 '13 at 3:43
• Voting to close, due to the OP's absence of reaction. – Did Feb 9 '13 at 16:50
• Yes, the question was correctly stated. Thanks for the hints. – user61147 Feb 12 '13 at 23:47
• No it was not, right now the domain is absurd. – Did Feb 14 '13 at 7:22