Prob & Stats, Lec 7B: Binomial Distribution (PMF, MGF, Mean, Variance), Intro to Negative Binomial

Описание: Do the probabilities from the Probability Mass Function (PMF) of a Binomial Distribution add to 1? We need the Binomial Theorem to prove this. The Binomial Theorem can also be used to find the Moment Generating Function (MGF) which, in turn, can be used to find the mean (expected value), variance, and standard deviation. Probabilities can be found with a graphing calculator, Excel, or Wolfram Mathematica. The Negative Binomial Distribution has a PMF that also involves a binomial coefficient, and we can use Excel or Mathematica to find probabilities. In both cases, we have independent and identical Bernoulli trials. With a Binomial RV, we are counting the number of successes in n trials. With a Negative Binomial RV, we are counting the number of trials until there are r successes. https://amzn.to/3rjDOoA (Probability and Statistics with Applications: A Problem Solving Text, by Asimow and Maxwell)

Calculus-based Probability and Statistics for Engineers and Scientists, Lecture 7, Part 2. Also for Data Scientists and Actuarial Science majors.

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