PROBABILITY: Distribution function

[tamintl]

Homework Statement

A continuous random variable X has density f(x) = ax²(1- x) for 0 < x < 1, and
f(x) = 0 otherwise. Here a is a constant, to be determined. Find the distribution func-
tion FX, the constant a, the expectation E(X), the variance Var(X), and the conditional
probability p(X < 1/2 | X > 1/4)

Homework Equations

The Attempt at a Solution

Really don't know where to start

 

[LCKurtz]

Start by using the fact that
$$\int_{-\infty}^\infty f(x)\,dx=1$$
to figure out a. Then use the standard formulas.