Question

1. Four coins are tossed. Let Z be the random variable representing the number of heads that occur. Find the values of the random variable Z. (you may extend the table or add column or row if needed)

Answer 1

For a toss of a coin, the outcome can be either a Head or a tail

When 4 coins are tossed the are 5 possible outcomes

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.

The 5 cases listed above explores all possible outcomes. Hence, the random variable Z takes any one value from

$\{0,1,2,3,4\}$