A discrete random variable X has the following probability distribution.
A discrete random variable X has the following probability distribution.
X | 1 | 2 | 3 | 4 | 5 | 6 | 7
P(X) | K | 2K | 2K | 3K | K² | 2K² | 7K² + K
What is the value of K?
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Correct answer: (C) 1/10
Explanation
The probabilities must add to 1: 9K + 10K² = 1, so 10K² + 9K − 1 = 0, i.e. (10K − 1)(K + 1) = 0. Since K > 0, K = 1/10.