Solution Found!
Let Xl . X2, be independent random variables that are
Chapter , Problem 5(choose chapter or problem)
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}.
Questions & Answers
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,