Examples of Forecasting with Bayes Theorem
Bayes theorem is an important tool for forecasting. The recent book by Nate Silver, "The Signal and the Noise" makes this point well. I suggest adding several example problems to this course to illustrate the use and power of Bayes Theorem as a forecasting tool. See, for example: http://allendowney.blogspot.com/2011/10/my-favorite-bayess-theorem-problems.html and http://www.math.hmc.edu/funfacts/ffiles/30002.6.shtml and several examples from the Nate Silver book. Consider integrating other material into the course, such as this video: http://www.khanacademy.org/math/applied-math/cryptography/random-algorithms-probability/v/bayes-theorem-visualized
Let me know if you see this as a valuable contribution to the course, if this is something you plan to do, or if you would like me to take the lead in this.
For events that are not disjoint, we end up with the following probability definition.
Actually the formula you show (with the subtraction of the combined events) in the next line is always correct. The simpler formula is just an instance of this where the subtracted term is zero. It may be helpful to mention this unification of the two formulas. --Lbeaumont (discuss • contribs) 21:39, 23 October 2013 (UTC)
The first paragraph in the "Random Variables" section does not seem related to random variables. What is the connection? Can you describe that connection more clearly? --Lbeaumont (discuss • contribs) 21:46, 23 October 2013 (UTC)
The section on Discrete and Continuous Random Variables includes the statement: For continuous random variables, we cannot list all possible values that a continuous variable can take because the number of values it can take is extremely large.
Indeed, the number of outcomes is infinite, not just extremely large. This should be rewritten to say: For continuous random variables, we cannot list all possible values that a continuous variable can take because the number of values it can take is infinite.
Add practice problems
This course is off to a good start. I believe it can be significantly enhanced if assignments requiring students to solve problems are included. Thanks for all your work on this. --Lbeaumont (discuss • contribs) 21:51, 23 October 2013 (UTC)