Doppler effect vibrato?

http://bottom-end.blogspot.com/2006/05/bernoulli-doppler-and-natural-vibrato.html

Gustavo Lacerda said...

I doubt the Doppler effect in your throat could be strong enough to be noticeable. For the first frequency doubling (octave), you'd need the sound source to be moving at half the speed of sound (i.e. v = 1/2 c). To triple the frequency (i.e. lambda = 3), you'd need it to move at 2/3 the speed of sound. In general, 1/lambda = 1-v/c, or v = c (1 - 1/lambda).

If we take the minimal noticeable change to be 20 cents (where 1200 is an octave), lambda = 1220/1200 = 61/60.
Thus v = c (1/61) = 1/61*340m/s ~= 5.57 m/s .

I don't think throats reach that speed when they vibrate.

I found that post by googling for Doppler effect + vibrato, because it's a cool idea.

a fundamental question about statistics

If you have the MLEs for all the parameters that describe the family of distributions under consideration, is it always the case that you can trivially combine them into the MLE of the distribution?

e.g.: Gaussians are parametrized by mean and variance, and the MLE Gaussian is the one with the MLE mean as its mean, and the MLE variance as its variance.

If the two parameters are independent, in the sense that likelihood(p1, p2) = likelihood(p1) likelihood(p2), then the hypothesis follows.