IB HL Maths - Statistics PDFs - continuous variables
This applet allows you to investigate Probability Density Functions (PDFs)
Enter a PDF in the f(x) input box and the range it operates on underneath.
(note this applet works only for single finite ranges).
Click restart to start on Step 1, and Click the next step button to advance.

Step 1 checks that the integral = 1. If not, this is not a proper PDF (also check f(x)≥0 for your range)
Step 2 calculates E(X) - also known as the mean, μ.
Step 3 finds the median
Step 4 discusses how to find the Mode
Step 5 finds the Variance, Var(X), σ² & Standard Deviation, σ
Step 6 finds the CDF - Cumulative Distirbution Function, F(x)
Example questions:
1. Find the constant a where f(x) = a.x² for 1<x<2
Find the mean, median and the mode
Find the Variance and the Standard Deviation
Find F(x), the CDF.
2. Do the same including find a where appropriate for
a) f(x) = a cos (x) for 0<x< π
b) f(x) = a e^x for 1<x<3
Do c) and d) in two separate tabs so you can compare the results
c) f(x) = a(x-9)² for 8<x<10
d) f(x) = a(x-1)² for 0<x<2
e) Compare you answers for c) & d). Which answers are the same, which are different.
Predict answers for f(x) = a(x-84)² for 83<x<85