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Question
If X is the random variable with distribution function F(x) given by,
F(x) = `{{:(0",", - oo < x < 0),(1/2(x^2 + x)",", 0 ≤ x ≤ 1),(1",", 1 ≤ x < oo):}`
then find P(0.3 ≤ X ≤ 0.6)
Solution
P(a ≤ X ≤ b) = F(b) – F(a)
P(0.3 ≤ X ≤ 0.6) = F(0.6) – F(0.3)
= `1/2 [(0.6)^2 + (0.6)] - 1/2 [(0.3)^2 + (0.3)]`
= `1/2 (0.96 - 0.39)`
= 0.285
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