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I have three Bernoulli variables:

$$X_1 \sim \text{Bernoulli}(p_1)$$ $$X_2 \sim \text{Bernoulli}(p_2)$$ $$X_3 \sim \text{Bernoulli}(p_3)$$

Dependency between them can be described by the $n$ observations, $n$ is large, in a form:

| X_1| X_2 | X_3 |
|----|---- |-----|
| 1  | 0   | 1   |
| 0  | 1   | 0   |
| 0  | 0   | 1   |
| 1  | 1   | 0   |
| 0  | 0   | 0   |
| 1  | 1   | 1   |
...

I would like to find the likelihood $p(\textbf{X} | \textbf{p})$ ?


I think I know how to find the $p(\textbf{X} | \textbf{p})$ if $X_1$, $X_2$ and $X_3$ are independent but they are dependent in this case.

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