PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Uncertainty in measurement
Mathematical Methods for Physics, Ch Probability, random variables and distributions
Problem
A telescope records 900 photons from a faint, steady star in one 10min exposure and 960 photons in a second 10min exposure of the same star, the photon arrivals being independent.
((a)) Find the standard deviation of each count and of the difference between them, and say whether the difference of 60 photons is evidence that the star brightened between the exposures.
((b)) Treating the two exposures as one 20min exposure, find the fractional uncertainty in the total count, and estimate the total exposure time needed at this rate to reduce it to 1 per cent.