Question

Following is the p. d. f. of a continuous r.v. X.

f(x) = `{(x/8,  "for"  0 < x < 4),(0,  "otherwise".):}`
Find expression for the c.d.f. of X.

Answer 1

c.d.f. of X
= F(X)

= `int_0^x x/(8)*dx`

= `(1)/(8) int_0^x x*dx`

= `(1)/(16)[x^2]_0^x`

= `(1)/(16)[x^2 - 0]`

= `x^2/(16)`.