6. Let X, X1, X2, . . . be random variables that take values in a metric space E with metric r. We say that (X,) converges in probability to X if for every & > 0. (3.51) lim P(r(X,, X) > 8) = 0. On the space of random variables taking values in E, define the metric d(X, Y) : = E(r(X, Y) Al). Show that (3.51) holds if and only if lim, d(X,, X) = 0