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Unformatted text preview: ECE 6010 Stochastic Processes Homework #3 Problems from Grimmet & Stirzaker: 1. Prob 2.7.4 a) P ( 1 2 < x 3 2 ) = F ( 3 2 ) F ( 1 2 ) = 1 2 . b) P (1 < X < 2) = F (2) F (1) = 1 2 . c) P ( Y X ) = P ( X 2 X ) = P ( X 1) = F (1) = 1 2 . d) P ( X 2 Y ) = P ( X 2 X 2 ) = P ( X 1 2 ) = 3 4 . e) P ( X + Y 3 4 ) = P ( X + X 2 3 4 ) = P ( X 1 2 ) = 1 4 f) P ( X Z ) = P ( X Z 2 ) = 1 2 z 2 if 0 z 2 . 2.Prob 2.7.7. Let T be the numbers of people on given typical flights of TWA, and B be the numbers of people on given typical flights of BA. P ( T = k ) = 10 k ! 9 10 k 1 10 10 k , P ( B = k ) = 20 k ! 9 10 k 1 10 20 k . Now P(TWA overbooked)= P(T=10)=( 9 10 ) 10 P(BA overbooked) = P ( B 19) = 20( 9 10 ) 19 ( 1 10 ) + ( 9 10 ) 20 , of which the latter is the larger. 1 3. Prob 2.7.9. (a) P ( X + x ) = ( if x < , F ( x ) x (b) P ( X x ) = ( if x < 1 lim y  x F ( y ) if x (c) P (  X  x ) = P ( x X...
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This note was uploaded on 03/01/2012 for the course ECE 6010 taught by Professor Stites,m during the Spring '08 term at Utah State University.
 Spring '08
 Stites,M

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