Responses1 page double spaces initial postAfter this write 2 reply on others discussionabout 100 words for each reply. Prompt:Do you think there is a difference between risk and uncertainty? If so, how would you characterize the difference?Do you think you can improve your chances of winning the state lottery? If so, why; if not, why not?Can you describe instances where a conditional probability is incorrectly treated as an unconditional probability?How do you think Bayes Theorem is used in economics? Can you find examples? How do you think it is used in machine learning? Can you find examples? LessonThis module begins the unit on probability and statistics. The first part of the unit covers probability basics the definition of probability, conditional probability, the definition and properties of random variables and their distributions, the calculation of expected values of a random variable, some special distributions, and finally, the laws of large numbers and the central limit theorem. Probability theory is the formal mathematical approach to addressing uncertainty. The two most prominent approaches to interpreting are the frequentist, and th
e subjectivist, sometimes known as the Bayesian approach. Probability theory does not depend on interpretation. Probability theory begins with a description of what is a sample space and what are events in the sample, both of which are based on set theory. As a result, we will review elementary set theory. Following our discussion of set theory, we will formally define probability. Next, we will define finite sample spaces. For finite sample spaces, we can use counting and combinatorial methods to calculate the probabilities. In these methods, we enumerate the events and use their relative frequency as the basis for calculating probabilities. We will then discuss conditional probabilities. This will give us the means to calculate unions of events as well as an avenue to define when events are independent of one another. Finally, we will discuss Bayes Theorem. Bayes Theorem underlies much of the current work on artificial intelligence and machine learning. Russell and Norvig in their book Artificial Intelligence assert it is a fundamental tool of adaptive reasoning systems. Answer preview
apa 200 words
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