Answered: For example: (6, 2, 2, 2, 6, 1, 1, 3,…

For example: (6, 2, 2, 2, 6, 1, 1, 3, 3, 3, 1, 3) has 7 runs: 2,2,2, 6, 1,1, 3,3, 3, 1 (Hint: a run either starts at the beginning or starts when aj-1 f a;)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Suppose that if I roll a sequence of 12 fair 6-sided dice a_1,\dots,a_{12}a1,…,a12. A run is a conguous subsequence of all the same number. What is the expected number of runs when you roll the sequence of 12 dice?

For example:
(6, 2, 2, 2, 6, 1, 1, 3, 3, 3, 1, 3)
has 7 runs:
6,2,2,2. 6 1,1, 3, 3, 3, 1
(Hint: a run either starts at the beginning or starts when a;-1 + a;)

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