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# Homework Assignments

## Homework 6

1. Suppose is a sequence of independent r.v.s each of which is uniformly distributed on the interval . Define a sequence of r.v.s by , where . Show that converges in distribution to an exponential r.v. with p.d.f.

2. Suppose (i.p.) and that there is a constant such that for all . Show that (m.s.)
3. Suppose (in distribution), where is a constant. Show that (i.p.)
Problems from Grimmet & Stirzaker
1. Exercise 7.2.1(b,c). On the converse, suppose takes values with probability 1/2.
2. Exercise 7.5.1.

Copyright 2008, Todd Moon. Cite/attribute Resource . admin. (2006, June 13). Homework Assignments. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/hw6.html. This work is licensed under a Creative Commons License