AS/A2 Stats 1 Stats 3

S2 Topic 2: Continuous random variables
Calculating probabilities 2
A pdf f(x) is defined by:

Find, using calculus, the probability of a value chosen at random from this distribution being less than 1.

Now find, again using calculus, the probability of a value chosen at random from this distribution being between 1 and 2.

Summary This method uses integration techniques from Pure 1. You will need to know how to integrate basic polyniomials in x such a linear, quadratic or cubic functions, and then how to substitute the limits. A note about graphic calculators A graphic calculator, for example the TI-83 or similar model, can work out definite integrals for you for you. Using the pdf defined above: P(X < 1) is given by fnInt((1/108)X(6-X)2,X,0,1) = .1319444444 P(1 < X < 2) is given by fnInt((1/108)X(6-X)2,X,1,2) = .275462963 This page uses WebEQ. To speed up downloading you can install this WebEQ Math Viewer . Click on the Math Viewer icon and you will be taken to the download site.