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Question
If the probability distribution of a random variable X is as given below:
Write the value of P (X ≤ 2).
| X = xi : | 1 | 2 | 3 | 4 |
| P (X = xi) : | c | 2c | 4c | 4c |
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
\[\Rightarrow c + 2c + 4c + 4c = 1\]
\[ \Rightarrow 11c = 1\]
\[ \Rightarrow c = \frac{1}{11}\]
\[\text{ Now } , \]
\[P\left( X \leq 2 \right) = P\left( X = 1 \right) + P\left( X = 2 \right) = \frac{1}{10} + \frac{2}{10} = \frac{3}{11}\]
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