d) (6 pts.) Online crowdsourcing has become a popular way to tackle problems that are (cur- rently) too complex to be pe

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D 6 Pts Online Crowdsourcing Has Become A Popular Way To Tackle Problems That Are Cur Rently Too Complex To Be Pe 1 (104.5 KiB) Viewed 99 times

d) (6 pts.) Online crowdsourcing has become a popular way to tackle problems that are (cur- rently) too complex to be performed by an algorithm but relatively simple for humans, such as detecting sarcasm on social media, solving protein folding puzzles, and classifying galax- ies. One project used crowdsourcing to classify night-time photographs taken by astronauts onboard the International Space Station. Volunteers were asked to identify what the pho- tographs contained: a city, stars, or an aurora. It is thought that 65% of the photos are of a city and 30% of the photos are of stars, with the remaining photos containing an aurora. Suppose that the photos with an aurora are always classified correctly and that photos with a city or stars are classified correctly 85% of the time. Photos with a city are classified as containing an aurora 2% of the time and photos with stars are classified as containing an aurora 6% of the time. If a photo is classified as containing stars, what is the probability that it actually shows a city? Be sure to show your work. e) (16 pts.) A galaxy cluster is an astronomical structure that contains anywhere from hun- dreds to thousands of galaxies bound together by gravity. Measurements of log-intensity (log number of photons) from small patches of the sky can be used to determine whether or not a galaxy cluster exists at a certain location. Galaxy clusters will emit a log-intensity that follows a normal distribution with mean 10 units and standard deviation 3 units. A log- intensity measurement from a part of the sky with no galaxy cluster present is distributed normally with mean 1 unit and standard deviation 1 unit. While there is no way of actually knowing if a galaxy cluster is located in a particular patch, an observation will be considered as having a galaxy cluster if the measured log-intensity has less than 0.02 probability of having come from a patch without a galaxy cluster. It is thought that the probability of a measurement actually being from a galaxy cluster is 0.01. i. Calculate the probability that an observation is considered as having a galaxy cluster. ii. Calculate the probability that an observation with log-intensity measurement greater than 3 units is from a galaxy cluster.