I am currently dealing with the joint density function of continuous random variables.

Here's the following piece-wise function I'm working on:

$$f(x,y)= \begin{cases} 24x & \text{if } 0 \le y \le 1-2x \text{ and } 0 \le x \le .5 \\ 0 & \text{otherwise} \end{cases}$$

Support of this pdf (not to scale): support using the bounds

How could I rearrange the bounds so that I could satisfy all of the y values in terms of x for the marginal PDF of random variable X?


The domain of interest is a triangle bounded by the $x$-axis, $y$-axis and the line $y=1-2x$.

Look at the what values does $y$ value take over the region. I will leave it as an exercise to figure out the two numbers, $c_1$ and $c_2$.

Once we fix the value of $y$, notice that $x$ can take any value between $0$ and $x=\frac{1-y}2$.

Hence $0 \le x \le \frac{1-y}2$ and $c_1 \le y \le c_2$,


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.