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प्रश्न
The probability density function of X is `f(x) = {(x, 0 < x < 1),(2 - x, 1 ≤ x ≤ 2),(0, "otherwise"):}`
Find P(0.5 ≤ X < 1.5)
उत्तर
P(0.5 ≤ X < 1.5) = `int_0.5^1 f(x) "d"x + int_1^(1.5) f(x) "d"x`
= `int_0.5^1 x "d"x + int_1^1.5 (2 -x) "d"x`
= `[x^2/2]_0.5^1 + [2x - x^2/2]_1^1.5`
= `1/2 - 0.25/2 + 3 - 2.25/2 - 2 + 1/2`
= `1 + 3 - 2 - 2.50/2`
= `2 - 2.5/2`
= `1.5/2`
= 0.75
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