01:960:285 Chapter Notes - Chapter 3: Mutual Exclusivity, Bayes Estimator, Conditional Probability

• School: Rutgers University
• Department: Statistics and Biostatistic
• Course: 01:960:285
• Professor: G. Popel

Document Summary

Chapter 3 intro to stats probability. In probability, we use the population information to infer the probable nature of the sample. P(a/b): baye"s rule (175) when an observed event a occurs with any one of several mutually exclusive and exhaustive events b1, b2, . bk. The formula for find the appropriate conditional probabilities is: given k mutually exclusive and exhaustive events b1, b2, . bk p(b1) + p(b2) + p(bk) = 1 and an observed event a then, p(bi/a) = p(bi upside u a)/p(a) =p(bi)p(a/bi)/p(b1(p(a/b1) + p(b2)p(b/b2) + . +p(bk)p(a/bk: combination rule (142) a sample of n elements is to be drawn from a set of n elements. Then, the number of different samples possible is denoted by (n (over ) n) and is equal to the below. Where the factorial symbol (!) means that n! = n(n-1)(n-2) . (3)(2)(1): (n = n!/n! (n-n): for example: 5! = 5 *4 *3 *2 *1 (note: the quantity 0!