a) Based on Table 1, find a recurrence relation for the number of bit sequences of length n with an odd number of 1s? b) Show that a, = 2" is a solution of the recurrence relation you obtained in (a).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 35E
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Question
No of bit
strings
2-2
2
2²-4
3 2²=8
b)
"1
1
N
52-32
List of outcomes
(1), (0)
(0,0), (0,1),(1,0), (1,1)
(0,0,0), (1,0,0), (0,1,0), (0,0,1), (1,1,0), (0,1,1), (1,0,1),(1,1,1)
(0,0,0,0), (1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1), (1,1,0,0), (0,1,1,0),
(0,0,1,1), (0,1,0,1), (1,0,1,0), (1,0,0,1), (0,1,1,1), (1,1,1,0), (1,0,1,1),
(1,1,0,1), (1,1,1,1)
(0,0,0,0,0), (1,0,0,0,0), (0,1,0,0,0), (0,0,1,0,0), (0,0,0,1,0), (1,1,0,0,0),
(0,1,1,0,0), (0,0,1,1,0), (0,1,0,1,0), (1,0,1,0,0), (1,0,0,1,0), (0,1,1,1,0).
(1,1,1,0,0), (1,0,1,1,0), (1,1,0,1,0), (1,1,1,1,0), (0,0,0,0,1), (1,0,0,0,1),
(0,1,0,0,1),(0,0,1,0,1), (0,0,0,1,1), (1,1,0,0,1), (0,1,1,0,1),(0,0,1,1,1),
(0,1,0,1,1), (1,0,1,0,1), (1,0,0,1,1), (0,1,1,1,1), (1,1,1,0,1), (1,0,1,1,1),
(1,1,0,1,1), (1,1,1,1,1)
a) Based on Table 1, find a recurrence relation for the number of bit sequences of
length n with an odd number of 1s?
Show that a = 2-¹ is a solution of the recurrence relation you obtained in (a).
Transcribed Image Text:No of bit strings 2-2 2 2²-4 3 2²=8 b) "1 1 N 52-32 List of outcomes (1), (0) (0,0), (0,1),(1,0), (1,1) (0,0,0), (1,0,0), (0,1,0), (0,0,1), (1,1,0), (0,1,1), (1,0,1),(1,1,1) (0,0,0,0), (1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1), (1,1,0,0), (0,1,1,0), (0,0,1,1), (0,1,0,1), (1,0,1,0), (1,0,0,1), (0,1,1,1), (1,1,1,0), (1,0,1,1), (1,1,0,1), (1,1,1,1) (0,0,0,0,0), (1,0,0,0,0), (0,1,0,0,0), (0,0,1,0,0), (0,0,0,1,0), (1,1,0,0,0), (0,1,1,0,0), (0,0,1,1,0), (0,1,0,1,0), (1,0,1,0,0), (1,0,0,1,0), (0,1,1,1,0). (1,1,1,0,0), (1,0,1,1,0), (1,1,0,1,0), (1,1,1,1,0), (0,0,0,0,1), (1,0,0,0,1), (0,1,0,0,1),(0,0,1,0,1), (0,0,0,1,1), (1,1,0,0,1), (0,1,1,0,1),(0,0,1,1,1), (0,1,0,1,1), (1,0,1,0,1), (1,0,0,1,1), (0,1,1,1,1), (1,1,1,0,1), (1,0,1,1,1), (1,1,0,1,1), (1,1,1,1,1) a) Based on Table 1, find a recurrence relation for the number of bit sequences of length n with an odd number of 1s? Show that a = 2-¹ is a solution of the recurrence relation you obtained in (a).
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