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.

Thank you ahead of time for the hints and answers.

  • $\begingroup$ What do you know about discrete rvs? $\endgroup$ – Alex Dec 8 '13 at 4:22
  • $\begingroup$ Yeah. I learned it. $\endgroup$ – KGTW Dec 8 '13 at 4:23
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    $\begingroup$ en.wikipedia.org/wiki/… for your first question $\endgroup$ – Alex Dec 8 '13 at 4:37
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    $\begingroup$ en.wikipedia.org/wiki/… for you second question $\endgroup$ – Alex Dec 8 '13 at 4:37

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