PÓLYA URN
Initial red balls a:
2
Initial blue balls b:
2
Reinforcement Δ:
1
Steps:
200
Runs:
10
Run / Add Runs
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Pólya urn process:
Start: a red, b blue
Draw ball, return it
+ Δ of same color
Limiting fraction X:
X ~ Beta(a/Δ, b/Δ)
E[X] = a/(a+b)
Var[X] = ab/((a+b)²(a+b+Δ))
Path-dependent! Each run
converges to a different
random limit. Martingale
convergence theorem applies.