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Question
The following is the p.d.f. of a r.v. X.
f(x) = `{(x/(8), "for" 0 < x < 4),(0, "otherwise."):}`
Find P(1 < X < 2),
Solution
P(1 < X < 2) = `int_1^2 f(x)*dx`
= `int_1^2 x/(8)*dx`
= `(1)/(8) int_1^2x*dx`
= `(1)/(16)[x^2]_1^2`
= `(1)/(16)[4 - 1]`
= `(3)/(16)`.
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