IE 111 HW10 - (b) E(x) = 7/12 (c) V(x) = 3/4 (7/12) 2 (d)...

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IE 111 HW#10 David Gritz 1. (a) 1 (b) 0/0.5=0 (c) Yes, the area is the same for both shapes showing the joint is the product of the marginals. (d) 0.25/0.5=.5 (e) 1.5/1=1.5 2. (a) F(y) = 4x 2 (b) F(y) = 4(x-0.25) 2 (c) F(y) = 4(x-0.125) 2 3. (a) Marginal (x) = x+1/2 ; Marginal (y) = y +1/2
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Unformatted text preview: (b) E(x) = 7/12 (c) V(x) = 3/4 (7/12) 2 (d) COV(x,y) = 19/144 4. (a) V(x+y)=V(x)+V(y)=2+8=10 (b) E(z+w) = 34 (c) COV(z,w) = E(zw) - E(z)E(w) = E(10x 2 + 21xy +2y 2 ) + E(10x+y) +E(x+2y) = 56...
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