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# 15 010 c x 2 025 030 020 what value of c makes it a

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Unformatted text preview: uppose f (x , y ) is deﬁned as, y 0 1 2 1 0.15 0.10 C x 2 0.25 0.30 0.20 What value of C makes it a valid p.m.f.? Find P (X > Y ) Find P (X + Y = 2) What are fx and fy ? What are E (X ) and E (Y )? What is E (X + Y )? Are X and Y independent? Culpepper, 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 Distributions, Deﬁnitions We can replace sums for integrals if X and Y are instead continuous random variables. A continuous joint p.d.f., f (x , y ), must satisfy the following properties, f (x , y ) ≥ 0 (f (x , y ) = 0 if (x , y ) is outside the support for X and Y ) ∞ ∞ f (x , y ) dxdy = 1 −∞ −∞ P [(X , Y ) ∈ A] = f (x , y ) dxdy A The marginal p.d.f.s are deﬁned as, ∞ f (x , y ) dy , x ∈ S1 (4) f (x , y ) dx , y ∈ S2 f1 (x ) = (5) −∞ ∞ f2 (y ) = −∞ X and Y are independent if f (x , y ) = f1 (x ) f2 (y ) Cul...
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