I'm working on the following problem, but I'm not really sure how to approach it - it's different from anything I've seen before! The problem is as follows: Consider the probability density function
$f_{X,Y}(x,y) = \left\{\frac{8+xy^3}{64}\right\}$ if $-1
, with probabilility $0$ otherwise.
What I'm trying to do is find the PDF of $W=2X+Y$, which is causing me some trouble - in fact I hardly know where to start! So I know the support of X is $-1
This is where I start to get confused. I believe in order to find the PDF, I first want to find the CDF of W, and then take the derivative of that. In order to find the CDF, I want to evaluate a double integral in terms of X and Y with the given PDF. However, I don't know what to set the bounds of these integrals to! In fact, I'm not really sure how to even begin; I feel like it might involve solving for X and Y in terms of W $(y=2x-w)$ and $(x=\frac{y-w}{2})$ but I don't know exactly what (if anything) to do with these!
Thank you so much for your help - I really appreciate it!
Sarah