Q. 4 A4.9( 20 Votes )

Find the probability distribution of

number of heads in two tosses of a coin.

Answer :

Given:

A coin is tossed twice. Hence, the sample space of the experiment is S = {HH, HT, TH, TT}


X represents the number of heads.


X(HH) = 2


X(HT) = 1


X(TH) = 1


X(TT) = 0


Therefore, X is a function on sample space whose range is {0, 1, 2}.


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


As we know,


P(HH) = P(HT) = P(TH) = P(TT) = 1/4


P(X = 0) = P(TT) = 1/4


P(X = 1) = P(HT) + P(TH) = 1/4 + 1/4 = 1/2


P(X = 2) = P(HH) = 1/4


Hence, the required probability distribution is,



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