An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, other wise X takes the value -1.The expected value of X, is:

The possibilities for getting one consecutive head are HTTTT, THTTT, TTHTT, TTTHT,TTTTH, HTHTT, HTTHT,HTTTH,THTHT,TTHTH,THTTH,HTHTH, 12 waysThe possibilities for getting two consecutive heads are HHTTT,THHTT,TTHHT,TTTHH,HHTHT,HHTTH,THHTH,HTHHT,HTTHH,THTHH, HHTHH, 11 waysThe possibilities for getting three consecutive heads are HHHTT,THHHT,TTHHH,HHHTH,HTHHH, 5 ways The possibilities for getting four consecutive heads are HHHHT, THHHH 2 ways The possibilities for getting five consecutive heads is HHHHHk = no. of times head occur consecutively Now expectation =∑XPk=−1×132+−1×1232+−1×1132+3×532+4×232+5×132=+18