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)

Cumulative Distribution Functions : Introduction : ExamSolutions - youtube Video

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)

Cumulative Distribution Function : Example : ExamSolutions - youtube Video