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Question
For the following probability density function of a random variable X, find P(X < 1).
`{:(f(x) = (x + 2)/18,";" "for" -2 < x < 4),( = 0,"," "otherwise"):}`
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Solution
P(X < 1) = `int_-2^1 (x + 2)/18 dx`
= `1/18 [x^2/2 + 2x]_-2^1`
= `1/18 {(1/2 + 2) - ((-2)^2/2 + 2(-2))}`
= `1/18 {5/2 + 2}`
= `1/18 xx 9/2`
= `1/4`
P(X < 1) = `1/4`
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