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Question
A discrete random variable X has the probability distribution given as below:
| X | 0.5 | 1 | 1.5 | 2 |
| P(X) | k | k2 | 2k2 | k |
Find the value of k
Solution
For a probability distribution, we know that if Pi ≥ 0
`sum_("i" = 1)^"n" "P"_"i"` = 1
⇒ k + k2 + 2k2 + k = 1
⇒ 3k2 + 2k – 1 = 0
⇒ 3k2 + 3k – k – 1 = 0
⇒ 3k(k + 1) – 1(k + 1) = 0
⇒ (3k – 1)(k + 1) = 0
∴ k = `1/3` and k = – 1
But k ≥ 0
∴ k = `1/3`
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