CCD Noise Levels

An infrared camera can operate with either of two CCDs, which reach a critical noise threshold either 1/2 or 2/3 of the time. You have a data set comprised of 300 frames, of which 175 reached the critical noise level. Which camera was most probably in the dewar during your observing run?

If p = 1/2, we expect P (300, 1/2)= 150.

If p = 2/3, we expect P (300, 2/3) = 200.

Hypothesis testing: We will decide after the experiment has taken place (after the observing run) which hypothesis (and thus which camera) to accept, when they are equally likely before the experiment. We calculate the maximum likelihood for each case.