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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 probability that X is between 1 and 3..
Solution
P(X is between 1 and 3) = P(1 < X < 3)
= `int_1^3 f(x).dx`
= `(1)/(64) int_1^3 x^3.dx`
= `(1)/(256)[x^4]_1^3`
=`(1)/(256)[81 - 1]`
= `(5)/(16)`.
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