Assignment Instructions/ Description
Image transcription textProblem 4. Flip a fair coin several times. Say that a changeover occurs whenever an outcome differs from
the one preceding it. For instance, if you flip the coin 5 times and the outcome is HHTHT, then there are 3
changeovers.
(i) Consider n independent flips of this coin. What is the expected number of changeovers?
Hint: For each flip, what is the probability that you observe a changeover? How can you decompose
the number of changeovers into a sum of bernoulli/indicator random variables?
(ii) If there are & changeovers, then the sequence of outcomes can be decomposed into & + 1 subsequences,
with each subsequence all heads or all tails, and the last subsequence of length 1. For example, the
following are outcomes with k = 2:
THT
HH TTT H
TTTTTTTTT HHHHHH T
What is the expected number of flips to get & changeovers?
Hint: How many flips are you doing before the next changeover? Can you model it as a known random
variable? Can you then express the number of flips you need to get & changeovers as a sum of known
random variables?... Show more�