# Multivariate Probability distribution

## Statistics study Log

# Sat, May 2

Read Ch. 5.3. It deals with conditional and marginal probability distributions. In the discrete case, it is not so difficult to understand. To acquire marginal density function from the joint probability distribution function, I sum $$p(y_1,y_2)$$ over y2.

Another topic in this chapter is how to acquire conditional probability function from marginal probability function and joint probability function. Basically, dividing the multivariate probability function by the marginal density function of y2 gives the probability of getting y1 given y2. Although a continuous case requires some theoretical considerations to apply this formula, practically it is okay to just apply this formula to both continuous and discrete functions.

# Textbook

Wackerly, D., Mendenhall, W., & Scheaffer, R. L. (2008). Mathematical Statistics with Applications (7 edition). Thomson Brooks/Cole. pp.223-295.