A coin is tossed n times (n > 4). What is the expected number of exactly three consecutive heads? Hint: Let E 1 be the event that the first three outcomes are heads and the fourth outcome is tails....

A coin is tossed n times (n > 4). What is the expected number of exactly three consecutive heads? Hint: Let E₁
be the event that the first three outcomes are heads and the fourth outcome is tails. For 2 ≤ i ≤ n − 3, let E_i
be the event that the outcome (i − 1) is tails, the outcomes i, (i + 1), and (i + 2) are heads, and the outcome (i + 3) is tails. Let E_n−2
be the event that the outcome (n − 3) is tails, and the last three outcomes are heads. Let

Then calculate the expected value of an appropriate sum of X_i’s.