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# 1 distributions of two random variables 42 the

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Unformatted text preview: Culpepper, SA STAT 400: Statistics and Probability I (7) Discrete Deﬁnitions Discrete Examples Continuous Deﬁnitions Continuous Examples 4.1: Distributions of two random variables 4.2: The Correlation Coeﬃcient Continuous Examples: P (X > Y ) 1. One easy approach, 1−y 0.5 x 2 ydxdy = P (X > Y ) = 60 0 y 11 16 (8) 2. Still an easier approach, 1−x 0.5 x 2 ydydx = 1 − P (X > Y ) = 1 − 60 0 x 11 5 = (9) 16 16 3. The more cumbersome approach, 0.5 x 0 = 1−x 1 x 2 ydydx + 60 P (X > Y ) = 60 0 x 2 ydydx 0.5 0 3 8 11 + = 16 16 16 Culpepper, SA (10) STAT 400: Statistics and Probability I Deﬁnitions Examples Predictions, Best Fit Line 4.1: Distributions of two random variables 4.2: The Correlation Coeﬃcient Example Bivariate Plot 6 q q q 5 Non−Smokers Smokers q Lung Capacity (l3) q 4 q q q 3 2 q 1 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q...
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