Four coin are tossed, let Z be the random variable representing the number of heads that turn up.find the value s of the random variable Z.

by tossing four coins, we may observe one of the following cases :

1. All the four outcomes are 'Tail'. So the 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.

Any 1 of the 4 outcomes is 'Tail' and the remaining three are 'Head' Hence, Z= 3 in this case.

All the four outcomes are 'Head'. So the number of heads is 4. Hence, Z= 4 in this case.

The 5 cases represent all the possible outcomes. Hence, the random variable Z takes any one value from {0,1,2,3,4}.