Intro to Stats, (most of) Lec 14A, Binomial Random Variables, Normal Approximations to Binomial RVs

(0:00) Schedule information.
(0:20) Outline of Lecture 14.
(1:20) Information about quizzes.
(1:50) Reminder to review Bayes' Rule (Bayes' Theorem) and practice problems related to it (using a Tree diagram is helpful).
(2:45) Binomial random variables.
(3:00) Review formula for binomial coefficients ("n choose k" = # of combinations of k objects from a group of n objects).
(5:40) Relationship between binomial coefficients and binomial distributions (random variables).
(7:09) Pascal's Triangle.
(8:58) Binomial Theorem.
(10:32) Binomial coefficient computation of 30 choose 14 using the formula and cancellation.
(15:26) Binomial "Setting" (when to use Binomial RVs).
(16:48) Compute a binomial probability with the formula when n = 4, p = 0.2, and k = 2.
(19:12) Mention that the Binomial Theorem can be used to confirm this is a valid probability model, meaning the probabilities are not only non-negative, but add up to 1 (you can think of this as a challenge problem if you are interested).
(20:30) Computing binomial probabilities on a spreadsheet with =BINOMDIST(k,n,p,cumulative). Pay attention to the nature of the inequality in the cumulative case.
(21:49) Do the spreadsheet calculations.
(26:14) Compute the mean in two ways: on the spreadsheet and with the special formula that works only for Binomial RVs.
(30:00) Normal approximation for a Binomial distribution (Internet business on-time shipping example). Finish the problem in the next video and review it in Lecture 14B.

#binomialdistribution #pascalstriangle #normalapproximation

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