**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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