# 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.

xyzP
0000.1
0010.2
0100.3
0110.4
1000.5
1010.6
1100.7
1110.8