<transcript><audio_28>to 2 and this is gonna be equal to 1 over 6 chance because it means you're rolling 4 on the dice I remember Y is simply going to be X well 6 minus X in this example so this is kind of the</transcript><transcript><audio_29>boundary populace we can make them a little bit complicated when we start combining them all together so we can combine the independent the minimum and the maximum all together in this very</transcript><caption><image_30>The image is a screenshot of a whiteboard with a list of equations written on it. The equations are written in black marker and are arranged in a neat and organized manner. The title of the image is "Combined them all together" and it appears to be a mathematical equation. The equation is written in red marker at the top of the page. Below the equation, there is a note that reads "Where op(s), op(t), and pg(t) are the constants of the equations. 

There are also two lines of text written on the whiteboard, one in blue and one in pink. The first line of text reads "Symmetry, the x-axis, and the y-axis. The second line is written below the equation in pink and blue. The third line is in green and the fourth line is blue.

The image appears to have been taken from a distance, as there are no other objects or objects visible in the background.</caption><transcript><audio_31>big formula over yeah as you can see we've got P we've got Q and then 1 minus P minus accused the independent and of course these values just have to meet certain requirements they both have to be between 0 and 1 and together</transcript><transcript><audio_32>they can't be greater than one but what is fascinating is how these things now relate to our correlation I mean we've got Spearman's Rho is equal to Q minus P and Kendall's tau is going to be equal</transcript><transcript><audio_33>to Q minus P times two plus P plus Q divided by three so we can take all the boundary copulas together and we can combine them into this formula over here which we can then use to try and represent other copula so of course this</transcript> to 2 and this is gonna be equal to 1 over 6 chance because it means you're rolling 4 on the dice I remember Y is simply going to be X well 6 minus X in this example so this is kind of the boundary populace we can make them a little bit complicated when we start combining them all together so we can combine the independent the minimum and the maximum all together in this very big formula over yeah as you can see we've got P we've got Q and then 1 minus P minus accused the independent and of course these values just have to meet certain requirements they both have to be between 0 and 1 and together they can't be greater than one but what is fascinating is how these things now relate to our correlation I mean we've got Spearman's Rho is equal to Q minus P and Kendall's tau is going to be equal to Q minus P times two plus P plus Q divided by three so we can take all the boundary copulas together and we can combine them into this formula over here which we can then use to try and represent other copula so of course this
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