chapter5m211

# chapter5m211 - Math 211 Introduction to Statistics Chapter...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 211 Introduction to Statistics Chapter 5 Probability and Some Probability Distributions Key words : Sample space, sample point, tree diagram, events, complement, union and intersection of an event, mutually exclusive events; Counting techniques: multiplication rule, permutation, combination, probability of an event; Additive rules; Conditional probability, independent events, multiplicative rules, Bayes’ rule. SAMPLE SPACE Sample Space. The set of all possible outcomes of a statistical experiment is called a Sample space. It is represented by the symbol S. Sample Point. Each outcome in a sample space is called an element or a sample point of the sample space. Example 1. (a) Consider the experiment of tossing a coin. The sample space S of possible outcomes may be written as S = { } , H T . (b) Consider the experiment of flipping a die. Then the elements of the sample space S is listed as S = { } 1,2,3,4,5,6 . (c) Now consider the experiment of tossing a die and then a coin once. The resultant sample space can be obtained using TREE DIAGRAM. That is, Therefore the sample sample S is S = { } 1 ,1 ,2 ,2 ,3 ,3 ,4 ,4 ,5 ,5 ,6 ,6 H T H T H T H T H T H T . Sonuc Zorlu Lecture Notes 1 Math 211 Introduction to Statistics Event. An event is a subset of a sample space. For example { } 4 ,6 A H T = is an event defined on S . One can define 12 2 events on S. Empty set ∅ , is an impossible event and S is a sure event. Any subset of S is represented by capital letters such as A, B, C… The Complement of an Event. The complement of an event A with respect to S is the subset of all elements of S that are not in A . The complement of A is denoted by the symbol ' A or c A . The Intersection of Events. The intersection of two events A and B, denoted by the symbol A B ∩ is the event containing all elements that are common to A and B. Mutually Exclusive Events. Two events A and B are mutually exclusive or disjoint if A B ∩ = ∅ , that is if A and B have no common elements in common. The Union of Events. The union of two events A and B, denoted by the symbol A B ∪ is the event containing all elements that belong to A or B or both . Important Notes. The following results may easily be verified by means of Venn diagrams. (1) A ∩ ∅ = ∅ (2) A A ∪ ∅ = (3) ' A A ∩ = ∅ (4) ' A A S ∪ = (5) ' S = ∅ (6) ' S ∅ = (7) ( 29 ' ' A A = (8) ( 29 ( 29 ' ' ' A B A B ∩ = ∪ 1 st De Morgan Rule (9) ( 29 ' ' ' A B A B ∪ = ∩ 2 nd De Morgan Rule Example 2. If { } 0,1,2,3,4,5,6,7,8,9 S = and { } 0,2,4,6,8 A = , { } 1,3,5,7,9 B = , { } 2,3,4,5 C = and { } 1,6,7 D = , list the elements of the sets corresponding to the following events: (a) A C S ∪ = (b) A B ∩ = ∅ ( A and B are mutually exclusive events) (c) { } ' 0,1,6,7,8,9 C = (d) ( 29 { } { } ( 29 { } { } { } { } ' 0,1,6,7,8,9 1,6,7 1,3,5,7,9 1,6,7 1,3,5,7,9 1,7 C D B ∩ ∪ = ∩ ∪ = ∪ = (e) ( 29 { } ' ' 0,1,6,7,8,9 S C C ∩ = = (f) { } { } { } ' 2,4 0,2,3,4,5,8,9 2,4 A C D A C ∩ ∩ =...
View Full Document

{[ snackBarMessage ]}

### Page1 / 18

chapter5m211 - Math 211 Introduction to Statistics Chapter...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online