33. A coin, which lands on heads with probability ????, is continually flipped. Compute the expected number
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33. A coin, which lands on heads with probability ????, is continually flipped.
Compute the expected number of flips that are made until a string of ???? heads in a row is obtained.
HINT: Condition on the time of the first occurrence of tails, to obtain the equation
????[????] = (1 − ????)(Σ ????ⁱ⁻¹ + ????[????]) + (1 − ????)(Σ ????ⁱ⁻¹ ????)
Simplify and solve for ????[????].
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