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Saddle?

@mllabovitz and I don't think that this is a saddle shaped distribution.

I think you'd need something like

$$ f(x,y) = a \times (x^2 - y^2 + 1) $$

(☝️ plus [0,1] boundary crap )

OR

you could have something like the one below if you just wanted a saddle point at zero

$$ f(x,y) = a \times (x^2 - y^3) $$

(☝️ plus [0,1] boundary crap )

live-session/02-random-variables.Rmd

Lines 208 to 220 in a1b5600

### Saddle Sores
Suppose that you know that two random variables, $X$ and $Y$ are jointly distributed with the following *pdf*:
\[
f_{X,Y}(x,y) =
\begin{cases}
a * x^{2} * y^{2} & 0 < x < 1, 0 < y < 1 \\
0 & otherwise
\end{cases}
\]
This joint pdf is similar to the pdf that you can visualize above, under the distribution called "saddle". The difference between this function and the image above is that the function bounds the with support of $x$ and $y$ on the range $[0,1]$. This is to make the math easier for us in the next step.

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