Find the mean number of heads in three tosses of a fair coin.


Given: A coin is tossed three times.

three coins are tossed simultaneously. Hence, the sample space of the experiment is S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}


X represents the number of heads.


As we see, X is a function on sample space whose range is {0, 1, 2, 3}.


Thus, X is a random variable which can take the values 0, 1, 2 or 3.


P(X = 0) = P(TTT)


P(X = 1) = P(TTH) + P(THT) + P(HTT)


P(X = 2) = P(THH) + P(HTH) + P(HHT)


P(X = 3) = P(HHH)


Hence, the required probability distribution is,


X



0



1



2



3



P(X)











Therefore mean μ is:






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