Exercise 4 (#5.6). Find an example of cumulative distribution functions G, G1, G2,.. on R such that (i) lim, l∞(Gn, G) is the distance defined in Exercise 1 and 0. is the sup-norm distance 0 but OM, (Gn,G) does not converge to 0, where Ом, defined as o.(F,G) = sup, |F(x) – G(x)| for any cumulative distribution functions F and G; (ii) limn QM. (Gn,G) = 0 but o (Gn, G) does not converge to 0. %3D

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Exercise 4 (#5.6). Find an example of cumulative distribution functions
G, G1, G2,... on R such that
(i) lim, Q.(Gn, G)
is the distance defined in Exercise 1 and o.. is the sup-norm distance
defined as o.(F,G) = sup |F(x) – G(x)| for any cumulative distribution
functions F and G;
0 but OM. (Gn,G) does not converge to 0, where
(ii) lim, QM, (Gn,G) = 0 but lo(Gn, G) does not converge to 0.
Transcribed Image Text:Exercise 4 (#5.6). Find an example of cumulative distribution functions G, G1, G2,... on R such that (i) lim, Q.(Gn, G) is the distance defined in Exercise 1 and o.. is the sup-norm distance defined as o.(F,G) = sup |F(x) – G(x)| for any cumulative distribution functions F and G; 0 but OM. (Gn,G) does not converge to 0, where (ii) lim, QM, (Gn,G) = 0 but lo(Gn, G) does not converge to 0.
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