Fully-Joint-Joint-Distribution
05-20-2022 || 15:37
Tags: #probability
fully-joint-joint-distribution
In fully joint joint distribution if there are 3 randome variables, they all are dependent on each other. So you have to calculate all the combinations to calculate the joint distribution.
Mathematically, for a 3 random variable joint distribution,
The formula will be,
$$
p(x,y,z) = p(x) p(y|x) p(z|x, y)
$$
To calculate this, if we have 2 possible output of each RV, we have to generate a table with $2^3$ rows.
| x | y | z | P |
|---|---|---|---|
| 0 | 0 | 0 | 0.1 |
| 0 | 0 | 1 | 0.2 |
| 0 | 1 | 0 | 0.3 |
| 0 | 1 | 1 | 0.4 |
| 1 | 0 | 0 | 0.5 |
| 1 | 0 | 1 | 0.6 |
| 1 | 1 | 0 | 0.7 |
| 1 | 1 | 1 | 0.8 |