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Question
The probability distribution of a random variable x is given as under:
P(X = x) = `{{:("k"x^2, "for" x = 1"," 2"," 3),(2"k"x, "for" x = 4"," 5"," 6),(0, "otherwise"):}`
where k is a constant. Calculate P(X ≥ 4)
Solution
Given that: P(X = x) = `{{:("k"x^2, "for" x = 1"," 2"," 3),(2"k"x, "for" x = 4"," 5"," 6),(0, "otherwise"):}`
∴ Probability distribution of random variable X is
| X | 1 | 2 | 3 | 4 | 5 | 6 | otherwise |
| P(X) | k | 4k | 9k | 8k | 10k | 12k | 0 |
We know that `sum_("i" = 1)^"n" "P"("X"_"i")` = 1
∴ k + 4k + 9k + 8k + 10k + 12k = 1
⇒ 44k = 1
⇒ k = `1/44`
P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6)
= 8k + 10k + 12k = 30k
= `30 xx 1/44`
= `15/22`.
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