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प्रश्न
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 the value of k .
उत्तर
We have,
The probability distribution of a random variable X is given below:
| x | 0 | 1 | 2 | 3 |
| P(X) | k |
\[\frac{k}{2}\]
|
\[\frac{k}{4}\]
|
\[\frac{k}{8}\]
|
\[ \text{ As } , \sum p_i = 1\]
\[ \Rightarrow k + \frac{k}{2} + \frac{k}{4} + \frac{k}{8} = 1\]
\[ \Rightarrow \frac{8k + 4k + 2k + k}{8} = 1\]
\[ \Rightarrow \frac{15k}{8} = 1\]
\[ \therefore k = \frac{8}{15}\]
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