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Update docusaurus/docs/protocol/primitives/probabilistic_proofs.md
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Co-authored-by: Bryan White <[email protected]>
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Olshansk and bryanchriswhite authored Dec 17, 2024
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Expand Up @@ -219,12 +219,11 @@ Recall:

#### Modeling a Dishonest Supplier's Strategy using a Geometric CDF (Cumulative Distribution Function)

Above, we have been tracking the probability that `Pr(X=k+1)`, the probability
of `k` failures (Supplier escapes without penalty) until a single success (Supplier)
is penalized. This can be modeled using a Geometric PDF (Probability Distribution Function).
So far, we've considered the probability given by `Pr(X=k+1)`: the probability
of `k` "failures" (👆) until a single "success" (👆). This can be modeled using a Geometric PDF (Probability Distribution Function).

In practice, we need to track the likelihood of `k or less` failures `Pr(X<=k)`,
until a single success. This can be modeled using a Geometric CDF.
In practice, we need to track the likelihood of `k or less` "failures" `Pr(X<=k)`,
until a single "success". This can be modeled using a Geometric CDF.

TODO_IN_THIS_PR: Remove the paragraph below. From Bryan: `This paragraph confuses me a bit. The previous paragraph says that we need to use a CDF but then this paragraph seems to turn around and say that this actually don't? I feel like this and the above paragraph should be combined and rephrased a bit.`

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