# probability density function and cumulative distribution function.

The Probability density function of a continuous random variable X is given by

$$f(x)=\left\{ \begin{array}{lr} cx^2 & 0≤x <1\\ c & 1≤x<2\\ c(3-x) & 2≤x<3\\ 0 & \text{otherwise} \end{array} \right.$$

There is three parts to this question.

(a) Find c. Which I found to be$$c= 6/11$$ (b)Calculate the cumulative distribution function F(x) of the random variable X.

(c) Calculate the expected value E(X) and the variance V(X)

I am having troubling finding the cumulative distribution function . Which is limiting me to only finding the answer to a.