The question is addressed below

Exercise 2 (10pts). A coin that lands on heads with probability p is continually flipped. Compute the expected number of flips that are made until a string of r heads in a row is obtained. (string of r heads means a successive sequence of r heads.) Hint: Condition on the time of the first occurrence of tails to obtain the equation E[X] =(1 -p) > p-'(i + E[X]) + (1 -p) _ pir i= i=r+1