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Question
A random variable has the following probability distribution:
| X = xi : | 1 | 2 | 3 | 4 |
| P (X = xi) : | k | 2k | 3k | 4k |
Write the value of P (X ≥ 3).
Solution
We know that the sum of probabilities in a probability distribution is always 1.
∴ P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4) = 1
\[\Rightarrow k + 2k + 3k + 4k = 1\]
\[ \Rightarrow 10k = 1\]
\[ \Rightarrow k = \frac{1}{10}\]
\[\text{ Now} , \]
\[P\left( X \geq 3 \right) = P\left( X = 3 \right) + P\left( X = 4 \right) = \frac{3}{10} + \frac{4}{10} = \frac{7}{10}\]
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