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Question
If X denotes the number on the upper face of a cubical die when it is thrown, find the mean of X.
Solution
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 = \[\sum\nolimits_{}^{}\] pixi = \[\frac{1}{6} + \frac{2}{6} + \frac{3}{6} + \frac{4}{6} + \frac{5}{6} + \frac{6}{6} = \frac{21}{6} = 3 . 5\]
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