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 denote the amount gained or lost by the person. Thus write the Range of Distribution

Sample Space $\left(\mathrm{S}\right)=\left\{ \mathrm{HHH}, \mathrm{HHT}, \mathrm{HTH}, \mathrm{THH}, \mathrm{HTT}, \mathrm{THT}, \mathrm{TTT} \right\}$

$$\begin{gathered} \mathrm{X}\left(\mathrm{HHH}\right)=2\times 3=6 \\ \mathrm{X}\left(\mathrm{HHT}\right)=\mathrm{X}\left(\mathrm{HTH}\right)=\mathrm{X}\left(\mathrm{THH}\right)=2\times 2-1\times 1.5 \\ =4-1.5 \\ =2.5 \\ \mathrm{X}\left(\mathrm{TTH}\right)=\mathrm{X}\left(\mathrm{THT}\right)=\mathrm{X}\left(\mathrm{HTT}\right)=2\times 1-2\times 1.5 \\ =2-3 \\ =-1\left(\mathrm{loss}\right) \\ \mathrm{x}\left(\mathrm{TTT}\right)=-3\times 1.5=-4.5\left(\mathrm{loss}\right) \end{gathered}$$

for each element of the sample space, X takes a unique value, Hence X is a function on the space whose range is $\left\{ -1, 2.50, -4.50, 6 \right\}$