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,