# STA Q1

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 Author: srod5409 ID: 90545 Filename: STA Q1 Updated: 2011-06-13 23:06:02 Tags: STA QUIZ Folders: Description: STA Q1 Show Answers:

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1. 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
2. Outcome
A particular result of an experiment. ␣ Ex: rolling a 3 on a dice is an outcome
3. Event
A collection of one or more outcomes of an experiment. Ex: 1,4,5
4. Sample space
The collection of all outcomes of an experiment␣ Denoted by S Ex:Is sample space an event? Yes.
5. Probability
• - A number between 0 and 1
• - Reflects the likelihood of occurrence of an event
6. 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
7. Empirical Probability
Definition: Number of times an event occurred divided by thetotal number of trials

Properties: determined a posteriori
8. 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=
9. Mutually Exclusive Events
• Events with no common outcomes
• Occurrence of one event excludes occurrence of theother
10. 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
11. Partition of Sample Space
Events are both mutually exclusive and collectively exhaustive
12. 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.
• P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
14. Addition Law; Mutually Exclusive Events Case
• If A and B are mutually exclusive, then P(A ∪ B) = P(A) + P(B)
15. 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 space
• You are blindfolded and asked to select a slice of
• pizza
• Event A = your slice contains pepperoni
• Event B = your slice contains mushroom
16. Probability Matrix
17. Conditional Probability
P(A| B) = P(A∩B) / P(B)
18. Multiplication Law
P(A∩ B) = P(A)⋅P(B | A)
19. Multiplication Law; Independent Events Case
If A and B are independent, then
P(A ∩ B) = P(A)· P(B)
20. Random Variables (R.V)
a variable whose value may change from one experimental unit to another
21. Discrete Distributions
• Discrete r.v. — takes on a finite or countably infinite number of possible values
• - Number of absent employees on a given day␣

Discrete distribution — probability distribution of a discrete r.v.
22. 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.
23. 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
24. 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

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