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..

Answer 1

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)`.