Simultaneous convoluted linear equations

#1
While doing an odds-to-probability derivation, I came upon an interesting relationship between x and y in a pair of simultaneous equations.

Care to solve for x and y..?

1561403856837.png

Hint: This avenue ended up being a dead-end, derivation-wise.

Thanks,

NLZS
 
#3
Bingo. Which is why my 'derivation' died. Thanks for confirming.

For kicks, I did a bunch of substitutions in Microsoft Word's 'Equation' function and ended up with some cool x = y formulas:

1561466224384.png

1561466254604.png
 
#5
Gee, I didn't know I was until I tripped on one.

Continued.fractions,9-6.jpg
But are these x=y relationships really a 'continued fraction', since the only variable (x or y as a-sub-n) is the one on the bottom of the inverted pyramid..? The other a-sub's (0, 1, 2..) are just '1'.
 
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#6
LINEAR vs NONLINEAR ODDS-TO-PROBS CONVERSION

As initially noted in this thread, in trying to establish the relationship between odds and probabilities through the linear model for a two-outcome event -- where Prob.1 + Prob.2 = 100% -- I’d reached the above dead-end-but-fun equations, trying to solve for the Odds Ratio (Odds.1/Odds.2).

Modeling the true relationship between odds and probabilities results in a simple nonlinear equation (fractional odds, no house take):



See: http://www.talkstats.com/threads/nonlinear-odds-to-probs-conversion.73716/
 

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