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Question
The p.d.f. of a continuous r.v. X is
f(x) = `{((3x^2)/(8), 0 < x < 2),(0, "otherwise".):}`
Determine the c.d.f. of X and hence find P(X < –2)
Solution
F(x) = `int_0^xf(x)*"d"x`
= `int_0^x (3x^2)/(8)*"d"x`
= `(3)/(8) int_0^x x^2*"d"x`
= `(1)/(8)[x^3]_0^x`
= `x^3/(8)`
P(X < – 2) = F(– 2)
F(x) = 0 ...`[("F"(x) = 0 "if" x ∉ (0,2)),(therefore "F"(x) = 1 "for" x ≤ 0)]`
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