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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(X < 1.5),
Solution
P(X < 1.5) = `int_0^1.5 f(x)*dx`
= `int_0^1.5 x/(8)*dx`
= `(1)/(8)int_0^1.5 *dx`
= `(1)/(16)[x^2]_0^1.5`
= `(1)/(16)[2.25 - 0]`
= `(2.25)/(16)`.
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