The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is

Let X be the random variable representing a number on the die

total number of observations=6

$$\begin{gathered} \mathrm{P}(\mathrm{X}=1)=\frac{3}{6}=\frac{1}{2} \\ \mathrm{P}(\mathrm{x}=2)=\frac{2}{6}=\frac{1}{3} \\ \mathrm{P}(\mathrm{X}=5)=\frac{1}{6} \end{gathered}$$

Now Mean $=\sum _{ }\mathrm{xP}\left(X\right)$

                    $$\begin{gathered} =1\left(\frac{1}{2}\right)+2\left(\frac{1}{3}\right)+5\left(\frac{1}{6}\right) \\ =\frac{12}{6} \\ =2 \end{gathered}$$