Statistics 270 - Lecture 19.

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Presentation transcript:

Statistics 270 - Lecture 19

Continue Chapter 5 today

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

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

More Generally

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

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

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

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