lecturenotesweek10

lecturenotesweek10 - ISyE 2027 Probability with...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ISyE 2027 Probability with Applications Polly B. He Fall10, Week 10 Reading: Section 9.1-9.3 Joint Distributions of Random Variables Examples of joint distributions of related random variables: 1. In a census, one may be interested in age, gender, income, etc. 2. In designing a new engine, one needs to consider the joint effects of wind speed, tem- perature, humidity, etc. 3. In medical studies, one is interested in a set of physiological variables of the patient population. The Discrete Case Definition: The joint probability mass function p of two discrete random variables X and Y is the function p : R 2 → [0 , 1], defined by p ( a, b ) = P ( X = a, Y = b ) ,-∞ < a, b < ∞ Example 9.1.1 A fair coin is tossed three times. Let X denote the number of heads on the first toss and the Y the total number of heads. What is the joint probability mass function of X and Y ? You can obtain the probability mass function for X (or Y ) by summing the joint probabilities in the rows (or columns). These are called the marginal probability mass functions ....
View Full Document

{[ snackBarMessage ]}

Page1 / 6

lecturenotesweek10 - ISyE 2027 Probability with...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online