zz-25 - ECE 6010 Stochastic Processes Homework#3 Problems...

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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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zz-25 - ECE 6010 Stochastic Processes Homework#3 Problems...

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