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Question
A random variable X has the following probability distribution :
| X = x | -2 | -1 | 0 | 1 | 2 | 3 |
| P(x) | 0.1 | k | 0.2 | 2k | 0.3 | k |
Find the value of k and calculate mean.
Solution
As the given table is probability distribution table :
∑pi = 1
∴ 0.1 + k + 0.2 + 2k + 0.3 + k = 1
∴ 0.6 + 4k = 1
∴ 4k = 1 - 0.6
∴ 4k = 0.4
∴ k = 0.1
k = 0.1
| X = x | -2 | -1 | 0 | 1 | 2 | 3 |
| P(x) | 0.1 | 0.1 | 0.2 | 0.2 | 0.3 | 0.1 |
E (X) (mean) = ∑pi xi
= - 0.2 - 0.1 + 0 + 0.2 + 0.6 + 0.3
= 0.8
∴ k = 0.1 and E(X) = 0.8
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