Find the probability distribution of
number of heads in four tosses of a coin.
When a coin is tossed four times, the sample space is
{HHHHHHHTHHTHHTHTHTTHHTTTTHHHHTHHTHHTTHTHHHTTTTHHTTHTTTTHTHTTTTTT }
which contains 16equally likely sample points.
Let X be the random variable, which represent the number of heads. It can be seen that X can take the value of 1,2,3, or 4.
P(X=0)=P (no head shows up) = P{TTTT} =116,
P(X=1)= P (one head and three tails show up)
= P(HTTT,THTT,TTHT,TTTH)=416=14,
P(X=2) =P (two heads and two tails show up)
= P({HHTT,HTHT,HTTH,THHT,THTH,TTHH}) =616=38,
P(X=3) =P (three heads and one tail show up)
= P({HHHT,HHTH,HTHH,THHH})= 416=14
and P(X=4)=P (four heads show up) = P({HHHH}) =116
Thus, the probability distribution is as follows:
X 0 1 234P(X)116 14 38 14116