A person plays a game of tossing a coin thrice. For each head, he is given Rs 2 by the organiser of the game and for each tail, he has to give Rs 1.50 to the organiser. Let X denotes the amount gained or lost by the person. Show that X is a random variable and exhibit it as a function on the sample space of the experiment.

Explanation

To solve the problem, we will first identify the sample space of the experiment and then define the random variable \(X\) based on the outcomes of tossing the coin thrice.

### Step 1: Determine the Sample Space
When a coin is tossed three times, the possible outcomes can be represented as follows:
- HHH (Head, Head, Head)
- HHT (Head, Head, Tail)
- HTH (Head, Tail, Head)
- HTT (Head, Tail, Tail)
...