How can I plot cdf of Y, Ft(t) using Matlab?

Conditions

1. Gaussian random vector A and B (in R3) are i.i.d.

2. A' and B' are unity norms and |A'| = |B'| = 1

3. Y = |A'(Transpose)*B'|^2 = cos^2(t)

How can I plot cdf of Y, Ft(t) using Matlab? Please help.

Answer 1

[Tom Lane]

Do you need a theoretical result? If not, can you just simulate A and B values, calculate Y, and plot its empirical cdf?

Either way, I'm not sure I understand the conditions. You say A and B are iid, but is each 3-vector in A assumed to have a 3-dimensional multivariate normal distribution with mean [0 0 0] and variance eye(3)? Then in condition 2, are you just saying that you need to divide each row by its norm so the vector lies on the unit sphere? If these are true, I hope that gives you an idea about how to simulate and plot them.