Let U1, U2, ... be i.i.d. Uni(0, 1) random variables. - log U; is distributed as exp(1). (2) Find the limit of the random sequence (U1U2 · · Un)"", as n → o. (3) Describe what happens to the sequence of random variables eVn (U¡U2 · · · Un)'/v™, (1) Show that X; as n → ∞?
Let U1, U2, ... be i.i.d. Uni(0, 1) random variables. - log U; is distributed as exp(1). (2) Find the limit of the random sequence (U1U2 · · Un)"", as n → o. (3) Describe what happens to the sequence of random variables eVn (U¡U2 · · · Un)'/v™, (1) Show that X; as n → ∞?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Let U1, U2, ... be i.i.d. Uni(0, 1) random variables.
- log U; is distributed as exp(1).
(2) Find the limit of the random sequence (U1U2 · · Un)/",
(3) Describe what happens to the sequence of random variables evn (U1U2· … Un)'/vn,
(1) Show that X;
as n → 0.
as n → ∞?
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