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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(1 < 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(1 < X < 2) = F(2) – F(1)
= `(2)^3/(8) - (1)^3/(8)`
= `1 - (1)/(8)`
= `(7)/(8)`
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