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Question
Find the mean of the following probability distribution:
| X= xi: | 1 | 2 | 3 |
| P(X= xi) : |
\[\frac{1}{4}\]
|
\[\frac{1}{8}\]
|
\[\frac{5}{8}\]
|
Solution
| xi | pi | pixi |
| 1 |
\[\frac{1}{4}\]
|
\[\frac{1}{4}\]
|
| 2 |
\[\frac{1}{8}\]
|
\[\frac{2}{8}\]
|
| 3 |
\[\frac{5}{8}\]
|
\[\frac{15}{8}\]
|
Mean = \[\sum\nolimits_{}^{}\] pixi = \[\frac{1}{4} + \frac{2}{8} + \frac{15}{8} = \frac{2 + 2 + 15}{8} = \frac{19}{8}\]
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