A galaxy cluster is an astronomical structure that contains anywhere from hun- dreds to thousands of galaxies bound toge
Posted: Thu Jul 14, 2022 4:52 pm
A galaxy cluster is an astronomical structure that containsanywhere from hun- dreds to thousands of galaxies bound together bygravity. Measurements of log-intensity (log number of photons) fromsmall patches of the sky can be used to determine whether or not agalaxy cluster exists at a certain location. Galaxy clusters willemit a log-intensity that follows a normal distribution with mean10 units and standard deviation 3 units. A log- intensitymeasurement from a part of the sky with no galaxy cluster presentis distributed normally with mean 1 unit and standard deviation 1unit.
While there is no way of actually knowing if a galaxy cluster islocated in a particular patch, an observation will be considered ashaving a galaxy cluster if the measured log-intensity has less than0.02 probability of having come from a patch without a galaxycluster. It is thought that the probability of a measurementactually being from a galaxy cluster is 0.01.
i. Calculate the probability that an observation is consideredas having a galaxy cluster.
ii. Calculate the probability that an observation withlog-intensity measurement greater than 3 units is from a galaxycluster.
While there is no way of actually knowing if a galaxy cluster islocated in a particular patch, an observation will be considered ashaving a galaxy cluster if the measured log-intensity has less than0.02 probability of having come from a patch without a galaxycluster. It is thought that the probability of a measurementactually being from a galaxy cluster is 0.01.
i. Calculate the probability that an observation is consideredas having a galaxy cluster.
ii. Calculate the probability that an observation withlog-intensity measurement greater than 3 units is from a galaxycluster.