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Question
If a random variable X has the following probability distribution:
| X : | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| P (X) : | a | 3a | 5a | 7a | 9a | 11a | 13a | 15a | 17a |
then the value of a is
Options
\[\frac{7}{81}\]
\[\frac{5}{81}\]
\[\frac{2}{81}\]
\[\frac{1}{81}\]
Solution
\[\frac{1}{81}\]
We know that the sum of probabilities in a probability distribution is always 1.
∴ P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4) + P (X = 5) + P (X = 6) + P (X = 7) + P (X = 8) = 1
\[\Rightarrow a + 3a + 5a + 7a + 9a + 11a + 13a + 15a + 17a = 1\]
\[ \Rightarrow 81a = 1\]
\[ \Rightarrow a = \frac{1}{81}\]
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