HW #3

(L) indicates light HW option (everyone should do), whereas (H) is for those pursuing the heavy HW option.

Problem 1 (L)

Pick a plot you would like to improve, and make it better.

1. 1. Show what you started with (if you had an original), or describe the problem you were trying to plot. 
   2. Describe the steps you went through to improve your plot
   3. Show final plot, and describe why it better answers your needs

Problem 2 (L)

Assume you are looking for faint gamma-rays in a gamma-ray spectrometer. The instrument works by looking at 1000k independent energy channels; and recording a hit in each channel. However, as always, there are both instrumental and environmental backgrounds. Assume you have a background rate per energy channel of 5.3 hits/channel in each 1 second measurement period.

1. 1. Assume you are looking for gamma-rays at a known energy (one channel), and your signal is steady in time. Pick an emission rate (0.1-10 gamma's per second), and calculate how long you would need to average to obtain a 5 sigma detection.
   2. Assume you are looking for rare bursts of gamma-rays at a known energy. For homework convenience, assume nature has provided gamma-ray bursts that are exactly as long as the integration time you found in part A. If you are searching through 2 months of data, how bright must a burst of gamma-rays be for you to have a 5 sigma detection? Compare to answer in part A.
   3. Now repeat problem B, but this time you don't know which of the 1000k energy channels the mono-energetic burst of gamma-rays might appear in.
   4. Describe (no need to actually do the calculation), how you would search for a burst of unknown duration, and how to determine the trials factor.

Problem 3 (H)

Take some of your data, and come up with a question or 'worry' that would require searching over multiple locations/times/parameters. 

1. 1. Come up with a parametrized model of your background. The more accurate the better, but if this will take too much time feel free to come up with a partial or toy model for this HW, just explain the corners you are cutting.
   2. Perform the search, including the trials factor. Describe what you find.