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(x < 1.5),

Answer 1

P(X < 1.5) = `int_0^1.5 f(x) .  dx`

= `int_0^1.5 x/(8)  .  dx`

= `(1)/(8)int_0^1.5  .  dx`

= `(1)/(16)[x^2]_0^1  .  5`

= `(1)/(16)[2.25 - 0]`

= `(2.25)/(16)`