Term

Definition
 outcome is uncertain
 shortrun proportion of occurences very random
 Long run more predictable
 Probability quantifies longrun randomness



Term

Definition
 as number of trials increase, proportion of occurrences of any given outcome approaches a particular number



Term

Definition
 outcome of any one trial is not affected by the outcome of nay other trial



Term

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

Definition
 Long run proportion of times that the outcome occurs in a very large number of trials



Term

Definition
 When longrun trials not feasible
 probability of outcome is your degree of belief the outcome will occur
 Bayesian statistics uses subjective probability.



Term

Definition
 For random phenomenon:
 sample space is the set of all possible outcomes



Term

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

Definition
 Probability of an event A = P(A)
 P(A) = (number of outcomes in event A)/(Number of outcomes in the sample space)



Term

Definition
 Complement of event A consists of all outcomes in sample space that are not in A
 Probabilities of A and of A^{c} (complement) sum to 1
 P(A^{c}) = 1 P(A)



Term

Definition
 events do not have any common outcomes



Term

Definition
 Outcomes that are common in both events



Term

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



Term

Definition
 For events A and B, Conditional probability of event A give that event B has occurred is
 P(AB) = P(A and B)/P(B)



Term
Pultiplication Rule for Finding P(A and B) 

Definition
 P(A and B) = P(AB) x P(B)
 P(A and B) = P(BA) 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(AB) = P(A) or P(BA)=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

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


