Question

If X denotes the number on the upper face of a cubical die when it is thrown, find the mean of X.

Answer 1

A cubical die can show 1, 2, 3, 4, 5 or 6 on its face.

xi	pi	pixi
1	\[\frac{1}{6}\]	\[\frac{1}{6}\]
2	\[\frac{1}{6}\]	\[\frac{2}{6}\]
3	\[\frac{1}{6}\]	\[\frac{3}{6}\]
4	\[\frac{1}{6}\]	\[\frac{4}{6}\]
5	\[\frac{1}{6}\]	\[\frac{5}{6}\]
6	\[\frac{1}{6}\]	\[\frac{6}{6}\]

Mean = \[\sum\nolimits_{}^{}\] p_ix_i = \[\frac{1}{6} + \frac{2}{6} + \frac{3}{6} + \frac{4}{6} + \frac{5}{6} + \frac{6}{6} = \frac{21}{6} = 3 . 5\]