Let Xl . X2, be independent random variables that are

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QUESTION:

Let Xl . X2, be independent random variables that are uniformly distributed over 1-1. 1]. Show that the seqllence Y1 , Y2 converges in probability to some limit, and identify the limit, for each of the following cases; (a) Yn = Xnln. (b) Yn = (Xn) n . (c) Yn = Xl ' X 2 . X n. (d) Yn = max{Xl" " , Xn}.

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QUESTION:

Let Xl . X2, be independent random variables that are uniformly distributed over 1-1. 1]. Show that the seqllence Y1 , Y2 converges in probability to some limit, and identify the limit, for each of the following cases; (a) Yn = Xnln. (b) Yn = (Xn) n . (c) Yn = Xl ' X 2 . X n. (d) Yn = max{Xl" " , Xn}.

ANSWER:

Step 1 of 6

Given that . be independent random Variables are uniformly distributed over

Let dative the sequence of $y_1, y_2 \ldots$ converges in probability to same limit and get the limit for given cases be.

(a)

(b)

(c)

(d)

So

and,

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