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प्रश्न
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"):}`
उत्तर
P(|X| < 1) = P(–1 < x < 1)
= `int_-1^1 (x + 2)/18 dx`
= `1/18 [x^2/2 + 2x]_-1^1`
= `1/18 {(1/2 + 2) - (1/2 - 2)}`
= `1/18 {5/2 + 3/2}`
= `1/18 xx 4`
= `2/9`
P(|X| < 1) = `2/9`
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