# Fully-Independent-Join-Distribution

05-20-2022 || 15:59
Tags: #probability

# fully-independent-join-distribution

In fully independent joint distribution, all of the random variables are independent and not dependent on each other. So they can be calculated on their own.

So if there are 3 random variables $(x_1, x_2, x_3)$ and there can 2, 3, 4 options respectively, then the equation will be,

$$p(x_1, x_2, x_3) = p(x_1) p(x_2) p(x_3)$$
For each of the needed parameters are,

• $p(x_1)$ - 2
• $p(x_2)$ - 3
• $p(x_3)$ - 4

So in total the number of parameters for $p(x_1, x_2, x_3)$ = 2 + 3 + 4 = 9

# References

joint-distribuition