1. Statistics Lecture 19

2. Continue Chapter 5 today

3. Definition
The marginal probability density function for continuous random variables X and Y, denoted by fX(x) and fY(y), respectively, are given by

4. Example:
The front tire on a particular type of car is suppose to be filled to a pressure of 26 psi
Suppose the actual air pressure in EACH tire is a random variable (X for the right side; Y for the left side) with joint pdf
Find the marginal distribution of X

5. More Generally

6. Independence
Two random variables X and Y are said to be independent if:
Discrete:
Continuous:

7. Example
Consider 3 continuous random variables X,Y, and Z with joint pdf:
X, Y and Z independent?

8. Conditional Probability
Let X and Y be rv’s with joint pdf f(x,y) and marginal distribution of X, f(x). The the conditional probability density of Y, given X=x is defined as
Substitute the pmf’s if X and Y are discrete

9. Example
Consider 2 continuous random variables X, and Y with joint pdf:
Find the marginal distribution of X
Find the conditional distribution of Y given X=0.2