the mean of the

Dear student,
In a die toss, the total number of outcomes = 6. Let X be the random variable representing a number on the die.
$$\begin{gathered} 1 appears on 3 faces, P (X=1) = \frac{3}{6} \\ 2 appears on 2 faces, P (X=2) =\frac{2}{6} \\ 5 appears on 1 face, P (X=5) = \frac{1}{6} \\ Given this distribution, we can calculate the Mean =1\times \frac{3}{6}+2\times \frac{2}{6}+5\times \frac{1}{6} \\ =\frac{3}{6}+\frac{4}{6}+\frac{5}{6} \\ =\frac{12}{6} \\ =2 \end{gathered}$$
$$\begin{gathered} Note: Mean of the probability distribution =\sum \left(X_i\times P\left(X_i\right)\right) \\ The Expected value of X is nothing but the mean of X. \end{gathered}$$
Regards