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:

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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 $$=$$∑$$XPk=$$−$$1$$×$$132+$$−$$1$$×$$1232+$$−$$1$$×$$1132+3$$×$$532+4$$×$$232+5$$×$$132=+18$$

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:

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