A galaxy cluster is an astronomical structure that contains anywhere from hundreds to thousands of galaxies bound togeth
Posted: Thu Jul 14, 2022 4:50 pm
A galaxy cluster is an astronomical structure that containsanywhere from hundredsto thousands of galaxies bound together by gravity. Measurements oflog-intensity(log number of photons) from small patches of the sky can be usedto determine whether ornot a galaxy cluster exists at a certain location. Galaxy clusterswill emit a log-intensity thatfollows a normal distribution with mean 10 units and standarddeviation 3 units. A logintensitymeasurement from a part of the sky with no galaxy cluster presentis distributednormally with mean 1 unit and standard deviation 1 unit.While there is no way of actually knowing if a galaxy cluster islocated in a particular patch,an observation will be considered as having a galaxy cluster if themeasured log-intensityhas less than 0.02 probability of having come from a patch withouta galaxy cluster. It isthought that the probability of a measurement actually being from agalaxy cluster is 0.01.i. Calculate the probability that an observation is considered ashaving a galaxy cluster.ii. Calculate the probability that an observation withlog-intensity measurement greaterthan 3 units is from a galaxy cluster.