Four coins are tossed. For each toss, the outcome belongs to one of the following:
{Head,Tail}
We want to count the total number of heads obtained from those 4 tosses.
Z is the random variable representing the number of heads that occur. We want to find the all possible values of Z.
Observe that, any one of the following cases may happen:
1. All the four outcomes are 'Tail'. So number of heads is 0. Hence, Z=0 in this case.
2. Any 3 of the 4 outcomes are 'Tail' and the remaining one is a 'Head' Hence, Z=1 in this case.
3. Any 2 of the 4 outcomes are 'Tail' and the remaining two are 'Head' Hence, Z=2 in this case.
4. Any 1 of the 4 outcomes is 'Tail' and the remaining three are 'Head' Hence, Z=3 in this case.
5. All the four outcomes are 'Head'. So number of heads is 4. Hence, Z=4 in this case.
Note that, the 5 cases listed above explores all possible outcomes.
Hence, the random variable Z takes any one value from {0,1,2,3,4}.