# 2 the correlation coecient discrete denitions

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Unformatted text preview: pepper, SA STAT 400: Statistics and Probability I 4.1: Distributions of two random variables 4.2: The Correlation Coeﬃcient Discrete Deﬁnitions Discrete Examples Continuous Deﬁnitions Continuous Examples Continuous Bivariate Expectations Expectations for continuous bivariate distributions are analogous to the discrete case. ∞ ∞ −∞ −∞ E [u (x , y )] = u (x , y ) f (x , y ) dxdy We can specify similar functions for u (x , y ) to obtain the marginal moments of X and Y or the ﬁrst order joint moment, E (XY ) Culpepper, SA STAT 400: Statistics and Probability I (6) 4.1: Distributions of two random variables 4.2: The Correlation Coeﬃcient Discrete Deﬁnitions Discrete Examples Continuous Deﬁnitions Continuous Examples Continuous Examples Suppose f (x , y ) is deﬁned as, f (x , y ) = Cx 2 y 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, x + y ≤ 1 0 otherwise Is f (x , y ) a valid p.d.f.? Compute the following: 1. 2. 3. 4. 5. P (X + Y < .5) P (X > Y ) P (2X ≤ Y ) What are the marginals for X and Y ? What are the means and variances of X and Y ? Are X and Y independent?...
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## This note was uploaded on 12/12/2013 for the course STAT 400 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

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