A number of 9 binary 0 or 1 digits is chosen at random with

A number of 9 binary (0 or 1) digits is chosen at random with all 2^9 possible results with equal probability. Let X be the random variable equal to the number of times \'010\' appears in the string. For example the binary string 010100101, X = 3 because there are 3 sets of \'010\' in the string. What is the expectation of X?

Solution

A number of 9 binary (0 or 1) digits is chosen at random with all 2^9 possible results with equal probability. Let X be the random variable equal to the number

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