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ENMA 420-520 Lecture 5 Slides_1

ENMA 420-520 Lecture 5 Slides_1 - Statistical Concepts for...

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Click to edit Master subtitle style 10/17/09 Statistical Concepts for Engineering Management ENMA 420 / 520 Lecture #5 Bivariate Probability Distributions and Sampling Distributions 11
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10/17/09 Joint Probability Distribution The joint probability distribution p(x,y) for two discrete random variables X and Y gives the values of p(x,y) for every combination of values of X and Y. Called a bivariate distribution Can be a table, graph or formula Requirements: 0 <= p(x,y) <= 1 for all values of X and Y 22
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10/17/09 Marginal and Conditional Probability Distributions Given discrete random variables X and Y and their joint probability distribution p(x,y): The marginal (or unconditional) probability distributions of X and Y are: The conditional probability distributions are given by: 33
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10/17/09 Exercise 6.2 44
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10/17/09 Exercise 6.2 (Cont’d) 55
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10/17/09 Exercise 6.6 Total Number of Combinations for 7 people & 3 positions: Then, need to determine the number of combinations of all three types for given X and Y. 66
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10/17/09 Exercise 6.6 (Cont’d) 77 Notice the “not enough” p(0,0) and “too many” cases p(3,1), P(2,3), and P(3,2).
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10/17/09 Exercise 6.6 (Cont’d) 88
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10/17/09 5-minute Break Discuss examples of joint probability distributions. 99
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10/17/09 Continuous Random Variables For continuous random variables X and Y: Bivariate joint probability density function: Marginal Density Functions: 1010
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10/17/09 Exercise 6.10 1111
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10/17/09 Exercise 6.12 1212
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10/17/09 Expected Value of Two Random Variables Given g(x,y), a function of two random variables X and Y, the expected value of g(X,Y) is: 1313
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