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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 ....
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- Fall '08