Distribution of sum and difference of X1 and X2

Use this diagram to illustrate the formulae for the mean and standard deviation of the sum and difference of two independent variables.

The long red vertical lines above the distributions of X1 and X2 can be dragged to adjust µ1 and µ2. The short red vertical lines can be dragged to change σ1 and σ2. The checkboxes at the top determine whether they can be independently changed.

Initially keep σ1 = σ2 and change µ1 and µ2, noting that the sd of the sum and difference are both sqrt(2) times σ1 (and σ2). Also mention that if µ1 = µ2, the difference has mean zero.

Click Accumulate and select several samples to demonstrate that the simulated data conform to the theoretical distributions.

Finally, allow different standard deviations and again alter the four parameters to illustrate the formulae for the parameters of the distribution of the sum and difference.