The cumulative distribution function, (c.d.f)

In the next tutorial I introduce you to the cumulative distribution function of a probability density function. All very confusing maybe but hopefully not after watching the next video. In it you will be shown how to do the following question.

Given

$f\left( x \right) = \left\{ \begin{array}{l} \frac{3}{8}{x^2},{\rm{ 0}} \le x \le 2\\ 0,{\rm{ otherwise}} \end{array} \right.$

i) Sketch the p.d.f. f(x)
ii) Find F(1)
iii) Find F(x)

Example

I have picked this next example as it has two functions in the p.d.f. and finding the c.d.f. can cause problems. Try it and check your answer against mine.

A continuous random variable X has a p.d.f. f(x), defined by

$f\left( x \right) = \left\{ \begin{array}{l} \frac{1}{4},{\rm{ 0}} \le x \le 1\\ \frac{{{x^3}}}{5},{\rm{ 1}} \le x \le 2\\ 0,{\rm{ otherwise}} \end{array} \right.$

Find the cumulative distribution function, F(x)

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