In game of throwing 3 coins, a player will loose Rs.5/- for each head and gain Rs.10/- for each tail. If a random variable $\mathrm{X} :\mathrm{S}\to \mathrm{R}$ is defined as $\mathrm{X}\left(\mathrm{a}\right)$ net gain $\left(\mathrm{a}\in \mathrm{S}\right),$ then the mean of the random variable is (in rupees)

If 3 coins are throw together, then 

sample space { HHH, HHT, HTH, HTT, THH, THT, TTH, TTT }

then X has value-15 (HHH), 0 (HHT, HTH, THH), 15 (HTT, THT, TTH) and 30 (TTT).

$\therefore$ Probability distribution is given by

$\therefore$ Mean  $=\sum \mathrm{x} \mathrm{P}\left(\mathrm{x}\right)$

                  $$\begin{gathered} =\frac{-15}{8}+0+\frac{45}{8}+\frac{30}{8} \\ =\frac{60}{8} \\ =\frac{15}{2} \end{gathered}$$