Question

The following is the p.d.f. of r.v. X:

f(x) = `x/8`, for 0 < x < 4 and = 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[x^2/2]_0^1.5`

= `(1.5)^2/16 - 0`

=`((9/4))/16`

= `9/64`.