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).

Answer 1

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)`.