Written assignment (Bayes' Rule) Bayes' Rule (also called Bayes' Theorem) is the foundation of Bayesian Statistics, a school of thought that's considered as fundamental to Probability as the...

Every thing you have to do is completely explained in the file I provided. This is to be completed by next week Friday
(9th of April).


Written assignment (Bayes' Rule) Bayes' Rule (also called Bayes' Theorem) is the foundation of Bayesian Statistics, a school of thought that's considered as fundamental to Probability as the Pythagorean Theorem is to Geometry. Though it is several centuries old, it's still relevant today in Artificial Intelligence as a prediction model. When applied to AI, events can be split into nodes in a graph to form a Bayesian Belief Network. Large machine learning applications will scale this very same algorithm up to hundreds or even thousands of variables, all to predict the probability of a single event! Description Use Bayes' Rule to solve the following word problems. Make sure you show your work! Problem #1 (2 pts) An estimated 7.7% of Americans have asthma. A recent report found that 20% of asthmatics (people who have asthma) smoke cigarettes. Comparatively, 92% of non-asthmatics do not smoke. What is the probability that a given person has asthma if they smoke? Problem #2 (2 pts) Suppose you have taken 20 exams this semester across all courses. Of those, you have passed 17 of them and failed 3. For 2 of your failed exams, you did not get enough sleep the night before. For 15 of your passed exams, you did get enough sleep the night before. With this information, what is the probability that you will pass your exam tomorrow if you plan on getting enough sleep tonight? Problem #3 (2 pts) A company manufactures a drug test which is undergoing clinical trials. 1,000 people are given the test, and 82 test results report "positive". Of those 82 people, 81 are in fact users of the drug. Among those who tested negative, 11 were users of the drug. Using this data, what is the probability that someone is a user of the drug if their test result comes back positive? Problem #4 (2 pts) An illness has a prevalence of 25% among the general population. A vaccine exists which prevents infection for 92% of those inoculated. It is estimated that 12% of the population is currently vaccinated. If someone contracts this illness, what is the probability that they were vaccinated? Problem #5 (2 pts) A local radio station has three DJ's. You know that the first DJ plays your favorite artist at least once 10% of the time, the second DJ 5% of the time, and the third DJ 35% of the time. Each DJ has a different time schedule. The first one controls 50% of total air time, the second 35%, and the third 15%. If you turn on the radio and hear your favorite artist, what is the probability that the third DJ is currently on the air? Hint Always start by isolating the hypothesis and evidence from the word problem. The hypothesis is what we are trying to prove and the evidence is how we are going to prove it. This means that the hypothesis is an unknown outcome whereas the evidence is known information. Once we know the hypothesis and the evidence, we can plug these into Bayes' Rule and solve for the requested value. This will always be the probability of the hypothesis given the evidence.