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

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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). Define 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
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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...
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