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Homework answers / question archive / If you have n independent flips of a coin with probability p of landing heads
If you have n independent flips of a coin with probability p of landing heads. And a changeover occurs whenever an outcome differs from the one preceding it. Ex: if n=5 and outcome is HHTHT then there are 3 changeovers.
We can express the number of changeovers as the sum of n-1 Bernoulli random variables.
What is the expected number of changeovers?
please see the attached file.
The probability of having a heads is p, thus the probability of landing tails is (1-p).
Let equal to 1 if a changeover occurs on the ith flip and 0 otherwise. Then
= 1* [ p{ i -1 is H, and H, i is T} + p{i-1 is T, i is H }]
+0* [ p{ i -1 is H, and H, i is H} + p{i-1 is T, i is T }]
