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Question
It is felt that error in measurement of reaction temperature (in celsius) in an experiment is a continuous r.v. with p.d.f.
f(x) = `{(x^3/(64), "for" 0 ≤ x ≤ 4),(0, "otherwise."):}`
Find P(0 < X ≤ 1).
Solution
P(0 < X ≤ 1) = `int_0^1f(x).dx`
= `int_0^1 x^3/(64).dx`
= `(1)/(64) int_0^1 x^3.dx`
= `(1)/(256)[x^4]_0^1`
= `(1)/(256)`.
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