# STA Q1

 The flashcards below were created by user srod5409 on FreezingBlue Flashcards. Experiment A process that leads to the occurrenceof one and only one of several possible observations. Ex: Rolling a die and recording the number of spots on the top face of the die Outcome A particular result of an experiment. ␣ Ex: rolling a 3 on a dice is an outcome Event A collection of one or more outcomes of an experiment. Ex: 1,4,5 Sample space The collection of all outcomes of an experiment␣ Denoted by S Ex:Is sample space an event? Yes. Probability - A number between 0 and 1- Reflects the likelihood of occurrence of an event Classical Probability Assumption: Definition: Number of outcomes leading to the event divided by the total number of possible outcomes Examples: probability of a head on a coin flip probability of a 3 on a die roll = Probability of S, P(S) =Properties: determined a priori objective Empirical Probability Definition: Number of times an event occurred divided by thetotal number of trials Properties: determined a posteriori Intersection of Events The intersection of two events, A & B, contains only the common outcomes in both events. Denoted as A∩B Examples: A = {1, 2, 4, 7, 9}, B = {2, 3, 4, 5, 6} A∩B=␣ A = {Blue, Purple, Red, White}, B = {Green, Red, Yellow} A∩B= Mutually Exclusive Events Events with no common outcomes Occurrence of one event excludes occurrence of theother Union of Events The union of two events, A & B, contains all the outcomes in both events. Denoted as A∪B Examples: A = {1, 2, 4, 7, 9}, B = {2, 3, 4, 5, 6} A∪B= 1,2,3,4,5,6,7,9 A A = {Blue, Purple, Red, White}, B = {Green, Red, Yellow} A∪B= Red Partition of Sample Space Events are both mutually exclusive and collectively exhaustive Complementary Events The complement of an event A is the event that A does not occur Denoted by Ac P(A) + P(Ac) = 1 A and Ac form a partition. Addition Law P(A ∪ B) = P(A) + P(B) – P(A ∩ B) Addition Law; Mutually Exclusive Events Case If A and B are mutually exclusive, then P(A ∪ B) = P(A) + P(B) Independent Events Occurrence of one event does not affect the occurrence/nonoccurrence of the other event The conditional probability of A given B is equal to the marginal probability of A.P(A | B)=P(A) Likewise, P(B | A)=P(B) The pizza represents the sample spaceYou are blindfolded and asked to select a slice ofpizzaEvent A = your slice contains pepperoniEvent B = your slice contains mushroom Probability Matrix Conditional Probability P(A| B) = P(A∩B) / P(B) Multiplication Law P(A∩ B) = P(A)⋅P(B | A) Multiplication Law; Independent Events Case If A and B are independent, then P(A ∩ B) = P(A)· P(B) Random Variables (R.V) a variable whose value may change from one experimental unit to another Discrete Distributions Discrete r.v. — takes on a finite or countably infinite number of possible values- Number of bad checks received by a restaurant- Number of absent employees on a given day␣ Discrete distribution — probability distribution of a discrete r.v. Continuous Distributions Continuous r.v. — takes on values at every point over a given interval- Elapsed time between arrivals of bank customers- Percentage of the labor force that is unemployed Continuous distribution — probability distribution of a continuous r.v. Binomial Distribution Binomial Distribution- Model experiment involving n independent identical trials- Each trial results in either success (S) or failure (F) Examples␣ Flipping a fair coin with “success = heads”␣ Rolling a die with “success = six ”␣ Conducting political opinion poll with “success = voting for a specific candidate”␣ Define X as total # of successes in n trials Normal Distribution Widely used to model natural characteristics ␣ height, weight, length ␣ IQ scores ␣ years of life expectancy␣ Many variables in business and industry are also normally distributed. ␣ annual cost of household insurance ␣ cost per square foot of renting warehouse space␣ amount of fill in soda cans ␣ Also referred to as Gaussian distribution Authorsrod5409 ID90545 Card SetSTA Q1 DescriptionSTA Q1 Updated2011-06-14T03:06:02Z Show Answers