Question: 1.*16. Convergence in pro for arbitrary r.v.'s may be reduced to that of bounded r. v.' s by the transformation X' = arctan X. In

1.*16. Convergence in pro for arbitrary r.v.'s may be reduced to that of bounded r. v.' s by the transformation X' = arctan X.

In a space of uniformly bounded r.v.'s, convergence in pr. is equivalent to that in the metric Po(X, Y) = cf(IX -YI); this reduces to the definition given in Exercise 8 of Sec. 3.2 when X and Y are indicators.

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