AS/A2 Stats 1 Stats 2

S3 Topic 1: Combinations of random variables
Graphing X-Y
The graphs of two Normal distributions are shown: X~N(m1,v1) in blue and Y~N(m2,v2) in red. Shown in black is the distribution of X-Y. Vary the values of m1, v1, m2 and v2 and see what effect they have on the combined graph.

Summary The mean of the combined distribution is the difference of the means of the individual distributions. However, the variance of the combined distribution remains the sum of the variances of the individual distributions. If X ~ N(m1,s12) and Y ~ N(m2,s22) then: X-Y ~ N(m1-m2,s12+s22) Based on free Java applets from JavaMath