I’d like to lead off with saying that this is a homework problem, in case that’s something anyone might want to avoid. Here is a link to the given information:
The issue that I’m having is that the pdf does not seem to be a consistent with the value I’m obtaining for $c$. In order to find the value of $c$, I took the integral of the pdf, from $-0.5$ to $0.5$, and I end up with with the integral being $2c/3$.
If I’m not mistaken, the integral of the pdf should be equal to 1, when all of the variable values are included. This being the case, $c$ would have to be $3/2$. However, if $c = 3/2$, then the pdf is $3/2 -6x^2$. Then, $f(X=0) = 3/2$.
This is where I’m currently at, and I’m trying to resolve places that I might have messed up. Is my integration incorrect? Or is my conceptual approach missing something? Alternatively, is this problem solvable? Assuming that I’ve done the above correctly, is there a way to manipulate the pdf/cdf to be correct? Any scaling or other methods to make it work?
Any and all help is appreciated!!