Find the probability distribution of

number of heads in four tosses of a coin.

Four tosses of a coin. Hence, the sample space of the experiment is S = {HHHH, HHHT, HHTH, HTHH, HTTH, HTHT, HHTT, HTTT, THHH, TTHH, THTH, THHT, THTT, TTHT, TTTH, TTTT}

X represents the number of heads.

As we see, X is a function on sample space whose range is {0, 1, 2, 3, 4}.

Thus, X is a random variable which can take the values 0, 1, 2, 3 or 4.

P(X = 0) = P(TTTT)

P(X = 1) = P(HTTT) + P(TTTH) + P(THTT) + P(TTHT)

P(X = 2) = P(HHTT) + P(THHT) + P(TTHH) + P(THTH) + P(HTHT) + P(HTTH)

P(X = 3) = P(THHH) + P(HHHT) + P(HTHH) + P(HHTH)

P(X = 4) = P(HHHH)

Hence, the required probability distribution is,

X | 0 | 1 | 2 | 3 | 4 |

P(X) | 1/16 | 1/4 | 3/8 | 1/4 | 1/16 |

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