We calibrate a detector to collect photons emitted from a faraway star whose temperature we want to estimate. The number of photons (m) of a particular wavelength detected during exposure time ot is distributed according to a geometric distribution m m P(m) = (1) m +1 m + 1 where m = 1/(e /T - 1) and O is assumed known at 2 x 103 K. T is the temperature. a) Verify that P(m) is normalized