Question: Suppose that a fair coin is tossed repeatedly until exactly k heads have been obtained. Determine the expected number of tosses that will be required.

Suppose that a fair coin is tossed repeatedly until exactly k heads have been obtained. Determine the expected number of tosses that will be required. Represent the total number of tosses X in the form X = X1 + . . . + Xk, where Xi is the number of tosses required to obtain the ith head after i − 1 heads have been obtained.

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