# Shared Flashcard Set

## Details

Stat 212
Exam 1 (Chapter 5)
22
Mathematics
09/29/2009

Term
 Random phenomena
Definition
 outcome is uncertain short-run proportion of occurences very random Long run more predictable Probability quantifies long-run randomness
Term
 Law of large numbers
Definition
 as number of trials increase, proportion of occurrences of any given outcome approaches a particular number
Term
 Independent Trials
Definition
 outcome of any one trial is not affected by the outcome of nay other trial
Term
 Finding Probabilities
Definition
 Calculate theoretical probabilities based on assupmtions about the random pehnomena Observe many trials of random phenomenon and use sample proportion of the number of occurences as probability
Term
 Relative frequency
Definition
 Long run proportion of times that the outcome occurs in a very large number of trials
Term
 Subjective probability
Definition
 When long-run trials not feasible probability of outcome is your degree of belief the outcome will occur Bayesian statistics uses subjective probability.
Term
 Sample Space
Definition
 For random phenomenon: sample space is the set of all possible outcomes
Term
 Event
Definition
 subset of sample space even corresponds to particular outcome or a group of possible outcomes
Term
 Probabilities for a sample space
Definition
 Each outcome in sample space has a probability The probability of each individual outcome is between 0 and 1 total of all individual probabilities equals 1
Term
 Probability of a Event
Definition
 Probability of an event A = P(A) P(A) = (number of outcomes in event A)/(Number of outcomes in the sample space)
Term
 Complement of events
Definition
 Complement of event A consists of all outcomes in sample space that are not in A Probabilities of A and of Ac (complement) sum to 1 P(Ac) = 1- P(A)
Term
 Disjointed EVents
Definition
 events do not have any common outcomes
Term
 Intersection of events
Definition
 Outcomes that are common in both events
Term
 Union of events
Definition
 Consists of outcomes that are in even A or B or in both A and B
Term
 Probability of Union of 2 events
Definition
 Addition Rule For the union of 2 events P(A or B) = P(a) + P(B) - P(A and B) If the events are disjoint, P(A and B) = 0 Thus: P(A or B) = P(A) + P(B)
Term
 Probability of Intersection of Two Events
Definition
 Multiplication Rule For the intersection of 2 independent Events A and B P(A and B) = P(A) X P(B)
Term
 Conditional Probability
Definition
 For events A and B, Conditional probability of event A give that event B has occurred is P(A|B) = P(A and B)/P(B)
Term
 Pultiplication Rule for Finding P(A and B)
Definition
 P(A and B) = P(A|B) x P(B) P(A and B) = P(B|A) x P(A)
Term
 Efinition of Independent Events using conditional probability
Definition
 2 events A and B are independent if probability that one occurs is not affected by the other Independent if P(A|B) = P(A) or P(B|A)=P(A) P(A and B) = P(A) x P(B)
Term
 Is a "Coincidence truly an unusual event?
Definition
 Law of very large numbers states that if something has a very large number of opportunities to happen, occasionally it will happen even if unusual
Term
 Probability Model
Definition
 specifies possible outcomes for sample space and provides assumptions on which probability calculations for events composed of these outcomes are based
Term
 carrying out a Simulation
Definition
 Identify random phenomenon to be simulated Describe how to simulate observations Carry out simulation many times Summarize results and state the conclusion
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