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two variables -> two parameters #26

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4 changes: 2 additions & 2 deletions contents/5.2.1.1-basic-concepts-to-review.md
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Expand Up @@ -114,7 +114,7 @@ Beta is my favorite distribution (what do you mean you don't have a favorite dis

Say, we have a coin with an unknown probability of turning heads. Let $$p$$ represent this probability. After $$n + m$$ flips, we get $$n$$ heads and $$m$$ tails. We might want to estimate that $$p = \frac{n}{n+m}$$. However, this is unreliable, especially if $$n+m$$ is small. We'd like to say something like this: $$p$$ can also be more than, less than, or equal to $$\frac{n}{n+m}$$, the values further away from $$\frac{n}{n+m}$$ having a smaller probability. And the higher the value of $$n+m$$, the higher the probability of $$p$$ being $$\frac{n}{n+m}$$. The beta distribution allows you to do that.

The beta random variable is represented using two variables: $$\alpha$$ to represent the number of successes and $$\beta$$ to represent the number of failures. The beta distribution can represent beyond coin flips. In fact, $$\alpha$$ and $$\beta$$ can rerepsent continuous value (though they can't be non-positive).
The beta random variable is represented using two parameters: $$\alpha$$ to represent the number of successes and $$\beta$$ to represent the number of failures. The beta distribution can represent beyond coin flips. In fact, $$\alpha$$ and $$\beta$$ can rerepsent continuous value (though they can't be non-positive).

$$
x \sim \text{Beta}(\alpha, \beta) \text{ with } 0 < \alpha, \beta \\
Expand Down Expand Up @@ -175,4 +175,4 @@ $$
A conditional probability distribution gives the probability of a subset of events occurring assuming that other events also occur. One example is $$P(X|Y)$$.

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*This book was created by [Chip Huyen](https://huyenchip.com) with the help of wonderful friends. For feedback, errata, and suggestions, the author can be reached [here](https://huyenchip.com/communication/). Copyright ©2021 Chip Huyen.*
*This book was created by [Chip Huyen](https://huyenchip.com) with the help of wonderful friends. For feedback, errata, and suggestions, the author can be reached [here](https://huyenchip.com/communication/). Copyright ©2021 Chip Huyen.*