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![[tex]X[/tex]](images/latex/b47736949a2a26fa60c778fc69b1a281d43b3a75_0.png "[tex]X[/tex]")
e ![[tex]Y[/tex]](images/latex/d547c9ed7793c8e2979684d0228219d9e95b7ad0_0.png "[tex]Y[/tex]")
dos variables aleatorias independientes uniformes e idénticamente distribuidas entre 0 y 1. Si ![[tex]G:=max[/tex]](images/latex/370b5a136c5a50f6edcbea8ea4b2075d7c75bde6_0.png "[tex]G:=max[/tex]")
{![[tex]X,Y[/tex]](images/latex/ab7787ccd4da6f06bebc398eccf61de74b611662_0.png "[tex]X,Y[/tex]")
}y ![[tex]C:=min[/tex]](images/latex/dbc5d59de915c2ea39ae1a2f9a9a094f1c22ca63_0.png "[tex]C:=min[/tex]")
{![[tex] f_{GC}(g,c) [/tex]](images/latex/fc87fc5fc5e9727adfeafa5433bce6e77305ffed_0.png "[tex] f_{GC}(g,c) [/tex]")
.
![[tex] X=Y=U(0,1)[/tex]](images/latex/3ec4e7f1e9575697354684441f03d5a1358a1897_0.png "[tex] X=Y=U(0,1)[/tex]")
![[tex]f_{G}(g)= 2[F(X=g)] f(X=g)[/tex]](images/latex/e50f99dbca426a278a852926e39bd99db0c7ac04_0.png "[tex]f_{G}(g)= 2[F(X=g)] f(X=g)[/tex]")
![[tex]f_{C}(c)= 2[1-F(X=c)] f(X=c)[/tex]](images/latex/3ead86e618210a2dc27bfc391afcfe54e7144fd4_0.png "[tex]f_{C}(c)= 2[1-F(X=c)] f(X=c)[/tex]")
![[tex]c \le g[/tex]](images/latex/29d0fc9f953f441ab300532a7981c01a580a1f84_0.png "[tex]c \le g[/tex]")
![[tex] F_{CG}(c,g) := P(G \le g, C \le c)[/tex]](images/latex/07ce1db767e321db148ae81fb32af58012db151f_0.png "[tex] F_{CG}(c,g) := P(G \le g, C \le c)[/tex]")
![[tex] F_{CG}(c,g)= P(X \le g, Y \le c) + P(Y \le g, X \le c) - P(X \le c, Y \le c)[/tex]](images/latex/d6e8e5e39ff5a8c4756d7677e548c5c67a6bf895_0.png "[tex] F_{CG}(c,g)= P(X \le g, Y \le c) + P(Y \le g, X \le c) - P(X \le c, Y \le c)[/tex]")
![[tex]F_{CG}(c,g)=F_{XY}(g,c) + F_{XY}(c,g) - F_{XY}(c,c) [/tex]](images/latex/bc618ef23776bcd83eff1a50102062d62f25989c_0.png "[tex]F_{CG}(c,g)=F_{XY}(g,c) + F_{XY}(c,g) - F_{XY}(c,c) [/tex]")
(*)
![[tex]F_{XY}(x,y)= \int_{-\infty}^{y} \int_{-\infty}^{x}1 dxdy [/tex]](images/latex/11cc6ff0f51fdae763fcf85473ba220a032f8e5a_0.png "[tex]F_{XY}(x,y)= \int_{-\infty}^{y} \int_{-\infty}^{x}1 dxdy [/tex]")
![[tex]F_{XY}(x,y)= xy , (x,y) \in I =\{(c,g) : 0 \le g \le 1, 0 \le c \le 1\} [/tex]](images/latex/28ece742a430d0fc29a3a08d4979aabb576573c9_0.png "[tex]F_{XY}(x,y)= xy , (x,y) \in I =\{(c,g) : 0 \le g \le 1, 0 \le c \le 1\} [/tex]")
![[tex]F_{CG}(c,g)= 2gc-c^2 ; (c,g) \in I : I= \{(c,g) : c \le g \le 1, 0 \le c \le 1\}[/tex]](images/latex/ac05f091c35a865bc5525a62c7935b9a6b46464e_0.png "[tex]F_{CG}(c,g)= 2gc-c^2 ; (c,g) \in I : I= \{(c,g) : c \le g \le 1, 0 \le c \le 1\}[/tex]")
![[tex]f_{CG}(c,g) = \frac{{\partial F_{GC}}}{{\partial g \partial c}}(c,g)[/tex]](images/latex/9f40c0db40ac01e103ced696272823cc5ccf63b9_0.png "[tex]f_{CG}(c,g) = \frac{{\partial F_{GC}}}{{\partial g \partial c}}(c,g)[/tex]")
![[tex]f_{CG}(c,g) =2 , (c,g) \in I: I = \{(c,g) : c \le g \le 1, 0 \le c \le 1\}[/tex]](images/latex/3b5ab01984dfd28d3050034b69daf4f03cb1f2bf_0.png "[tex]f_{CG}(c,g) =2 , (c,g) \in I: I = \{(c,g) : c \le g \le 1, 0 \le c \le 1\}[/tex]")
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