# Probability (P1 Exam Practice) - Multivariate Distributions I

Probability Exam P1 Practice

Now we are getting into the stuff for college students in level four undergraduate classes. There are many videos online on khan academy for calculus if you are pursuing a great career, including actuarial, option trading, engineering, etc.

Multivariate distributions depend on a lot of calculus and summations. You really need to be able to integrate and derive well. You can have multiple variables that vary on continuous or discrete properties and dependence. We will look at as many examples as possible so we can do our best on this exam.

# Bivariate Distribution Basics

This is exactly as it sounds. Joint probability distributions with two variables. You either need to have the following memorized or know exactly what it means.

### Equations and Rules for Continuous Joint Probability Functions

### Example 1

(a) Find k.

(b) What is the chance that X exceeds 3?

(c) Find Pr( x < 3 and y > 7).

### Equations and Rules for Discrete Joint Probability Functions

These follow from the continuous rules, but have summations because you are using whole numbers 0, 1, 2, ...

### Example 2 Mixed Continuous and Discrete

X is discrete with potential values {1, 5} and y is continuous between the values (2, 3).

Let us use the same function that we used in example 1 with the different conditions.

(a) Find k.

(b) What is the chance X = 1?

(c) What is the probability that X = 5 and Y > 2.5?

*Keep Learning Steemers!*