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(1 < x < 2)

Answer 1

P(1 < X < 2) = `int_1^2 f(x).dx`

= `int_1^2 x/(8).dx`

= `(1)/(8) int_1^2x.dx`

= `(1)/(16)[x^2]_1^2`

= `(1)/(16)[4 - 1]`

= `(3)/(16)`