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Question
The probability distribution of a random variable X is given below:
| x | 0 | 1 | 2 | 3 |
| P(X) | k |
\[\frac{k}{2}\]
|
\[\frac{k}{4}\]
|
\[\frac{k}{8}\]
|
Determine P(X ≤ 2) and P(X > 2) .
Solution
We have,
The probability distribution of a random variable X is given below:
| x | 0 | 1 | 2 | 3 |
| P(X) | k |
\[\frac{k}{2}\]
|
\[\frac{k}{4}\]
|
\[\frac{k}{8}\]
|
\[ \text{ As } , P\left( X \leq 2 \right) = 1 - P\left( X = 3 \right)\]
\[ = 1 - \frac{k}{8}\]
\[ = 1 - \frac{8}{15 \times 8}\]
\[ = 1 - \frac{1}{15}\]
\[ = \frac{14}{15}\]
\[\text{ Also} , P\left( X > 2 \right) = P\left( X = 3 \right)\]
\[ = \frac{8}{15 \times 8}\]
\[ = \frac{1}{15}\]
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