zz-15 - C such that | X n | C for all n . Show that X n X...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Utah State University ECE 6010 Stochastic Processes Homework # 6 Due Friday October 28, 2005 1. Suppose { X n } ) n =1 is a sequence of independent r.v.s each of which is uniformly dis- tributed on the interval (0 , 1). De±ne a sequence of r.v.s { Z n } by Z n = n (1 - Y n ), where Y N = max 1 i n X i . Show that { Z n } n =1 converges in distribution to an exponential r.v. with p.d.f. f ( x ) = ( e - x x 0 0 otherwise . 2. Suppose X n X (i.p.) and that there is a constant
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: C such that | X n | C for all n . Show that X n X (m.s.) 3. Suppose X n C (in distribution), where C is a constant. Show that X n C (i.p.) Problems from Grimmet & Stirzaker 1. Exercise 7.2.1(b,c). On the converse, suppose X n takes values 1 with probability 1/2. 2. Exercise 7.5.1. 1...
View Full Document

Ask a homework question - tutors are online