Given below is the probability distribution of a discrete random variable x. X 1 2 3 4 5 6 P(X = x) K 0 2K 5K K 3K Find K and hence find P(2 ≤ x ≤ 3) - Mathematics and Statistics

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Sum

Given below is the probability distribution of a discrete random variable x.

X 1 2 3 4 5 6
P(X = x) K 0 2K 5K K 3K

Find K and hence find P(2 ≤ x ≤ 3)

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Solution

We have `sumP(X = x)` = 1

∴ K + 0 + 2K + 5K + K + 3K = 1

∴ 12K = 1,

∴ K = `1/12`

Hence the probability distribution is

X 1 2 3 4 5 6
P(X = x) `1/12` 0 `2/12` `5/12` `1/12` `3/12`

∴ P(2 ≤ x ≤ 3) = P(x = 2) + P(x = 3)

= `0 + 2/12`

= `1/6`

Concept: Probability Distribution of Discrete Random Variables
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