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(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(X < – 2)  = F(– 2)

F(x) = 0       ...`[("F"(x) = 0  "if"  x ∉ (0,2)),(therefore "F"(x) = 1  "for"  x ≤ 0)]`