Chapter 14 From Randomness to Probability Dealing with Random Phenomena simulation , Apuntes de Estadística

¡Descarga Chapter 14 From Randomness to Probability Dealing with Random Phenomena simulation y más Apuntes en PDF de Estadística solo en Docsity! Chapter 14 From Randomness to Probability Dealing with Random Phenomena simulation •  A random phenomenon is a situation in which we know what outcomes could happen, but we don’t know which particular outcome did or will happen. •  In general, each occasion upon which we observe a random phenomenon is called a trial. •  At each trial, we note the value of the random phenomenon, and call it an outcome. •  When we combine outcomes, the resulting combination is an event. •  The collection of all possible outcomes is called the sample space. The Nonexistent Law of Averages •  The LLN says nothing about short-run behavior. •  Relative frequencies even out only in the long run, and this long run is really long (infinitely long, in fact). •  The so called Law of Averages (that an outcome of a random event that hasn’t occurred in many trials is “due” to occur) doesn’t exist at all. Modeling Probability (cont.) •  The probability of an event is the number of outcomes in the event divided by the total number of possible outcomes. P(A) = # of outcomes in A # of possible outcomes The First Three Rules of Working with Probability •  The most common kind of picture to make is called a Venn diagram. •  We will see Venn diagrams in practice shortly… simulation Formal Probability (cont.) 3.  Complement Rule: §  The set of outcomes that are not in the event A is called the complement of A, denoted AC. §  The probability of an event occurring is 1 minus the probability that it doesn’t occur: P(A) = 1 – P(AC) Formal Probability (cont.) 4.  Addition Rule: –  Events that have no outcomes in common (and, thus, cannot occur together) are called disjoint (or mutually exclusive). Formal Probability (cont.) 4.  Addition Rule (cont.): –  For two disjoint events A and B, the probability that one or the other occurs is the sum of the probabilities of the two events. –  P(A ∪ B) = P(A) + P(B), provided that A and B are disjoint. Formal Probability (cont.) 5.  Multiplication Rule: –  Many Statistics methods require an Independence Assumption, but assuming independence doesn’t make it true. –  Always Think about whether that assumption is reasonable before using the Multiplication Rule. Formal Probability - Notation Notation alert: •  In this text we use the notation P(A ∪ B) and P(A ∩ B). •  In other situations, you might see the following: – P(A or B) instead of P(A ∪ B) – P(A and B) instead of P(A ∩ B) Putting the Rules to Work •  In most situations where we want to find a probability, we’ll use the rules in combination. •  A good thing to remember is that it can be easier to work with the complement of the event we’re really interested in.