# PROBABILITY: Distribution function

1. Nov 14, 2011

### tamintl

1. The problem statement, all variables and given/known data
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)

2. Relevant equations

3. The attempt at a solution
Really dont know where to start

2. Nov 14, 2011

### LCKurtz

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