AS/A2 Stats 1 Stats 3

S2 Topic 2: Continuous random variables
PDFs 3
The following graph shows the pdf f(x) defined by:
a can be varied. Also shown is the cumulative probability function F(x) in red. This graph shows the total area under the pdf curve - ie., the total probability. Adjust a so that the total area under the pdf between 0 and 2 is 1. What is the value of E(X) for this pdf?

Answers The value required for a is 0.75. To verify this value precisely you would need to use calculus. Because of the symmetry of the graph, the value of E(X) is clearly 1. Based on free Java applets from JavaMath