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Question
A random variable X has the following probability distribution:
| Values of X : | −2 | −1 | 0 | 1 | 2 | 3 |
| P (X) : | 0.1 | k | 0.2 | 2k | 0.3 | k |
Find the value of k.
Solution
We know that the sum of probabilities in a probability distribution is always 1.
∴ P (X = -2) + P (X =-1) + P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) = 1
\[\Rightarrow 0 . 1 + k + 0 . 2 + 2k + 0 . 3 + k = 1\]
\[ \Rightarrow 4k + 0 . 6 = 1\]
\[ \Rightarrow k = \frac{0 . 4}{4} = 0 . 1\]
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