Question

The p.d.f. of a continuous r.v. X is

f(x) = `{((3x^2)/(8), 0 < x < 2),(0, "otherwise".):}`
Determine the c.d.f. of X and hence find P(1 < X < 2)

Answer 1

F(x) = `int_0^xf(x)*"d"x`

= `int_0^x (3x^2)/(8)*"d"x`

= `(3)/(8) int_0^x x^2*"d"x`

= `(1)/(8)[x^3]_0^x`

= `x^3/(8)`

P(1 < X < 2) = F(2) – F(1)

= `(2)^3/(8) - (1)^3/(8)`

= `1 - (1)/(8)`

= `(7)/(8)`