Lecture 02-probability - 1036: Probability & Statistics...

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Prob. & Stat. Lecture02 - probability (cwliu@twins.ee.nctu.edu.tw) 2-1 1036: Probability & Statistics 1036: Probability & 1036: Probability & Statistics Statistics Lecture 2 Lecture 2 -- -- Probability Probability
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Prob. & Stat. Lecture02 - probability (cwliu@twins.ee.nctu.edu.tw) 2-2 Sample Space • The set of all possible outcomes of a statistical experiment is called the sample space and is represented by the symbol S – Each outcome in S is called an element or a member of the sample space, or called sample point . – In most cases, the outcomes will depend on chance and, therefore, cannot be predicted with certainty. – The sample space may have infinite elements –E x am p l e : Consider the experiment of tossing a die • If we are interested in number that shows on the top face, Î S 1 = {1,2,3,4,5,6} • If we are interested whether the number is even or odd Î S 2 = {even, odd}
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Prob. & Stat. Lecture02 - probability (cwliu@twins.ee.nctu.edu.tw) 2-3 Tree Diagram • For small or finite number of elements, tree diagram is used to list the elements of the sample space systematically •F o r e x a m p l e s : D: defective, N: non-defective 3 random selected items H: head, T: tails Conditional flip a coin twice, or flip a coin once followed by tossing a die
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Prob. & Stat. Lecture02 - probability (cwliu@twins.ee.nctu.edu.tw) 2-4 Statement/Rule of Sample Space • Sample spaces with a large or infinite number of elements are best described by a statement or rule. • By using statement: •B y u s i n g r u l e } million 1 over population a city with a is | { x x S = } 1 | ) , ( { 2 2 + = y x y x S
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Prob. & Stat. Lecture02 - probability (cwliu@twins.ee.nctu.edu.tw) 2-5 Events An event is a subset of a sample space – e.g. the elements in which we are interested form an event. – A null set and the entire sample space S are also events •T h e complement of an event A , denoted by A’ , with respect to S is the subset of all elements of S that are not in A . – The complement of the null set is just the entire sample space h e intersection of two events A and B , denoted by A B, is the event containing all elements that are common to A and B. Two events A and B are called mutually exclusive , or disjoint , if A and B have no elements in common. That is A B= . h e union of the two events A and B , denoted by A B, is the event containing all the elements that belong to A or B or both.
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Prob. & Stat. Lecture02 - probability (cwliu@twins.ee.nctu.edu.tw) 2-6 Example: Venn Diagram In Venn diagram, the sample space S is illustrated by a rectangle. All the events are represent by circles. 2 and 2,6, region ) ( 1 region 7 and 4 region 7 and 1,2,3,4,5, region 3 and 1 region 2 and 1 region = = = = = = C B A C B A A B C A C B B A
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Prob. & Stat. Lecture02 - probability (cwliu@twins.ee.nctu.edu.tw) 2-7 De Morgan Laws • De Morgan’s first law: •D e M o r g a n s s e c o n d l a w : I U n i i n i i E E B A B A 1 1 , ) ( = = = = U I n i i n i i E E B A B A 1 1 , ) ( = = = =
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Prob. & Stat. Lecture02 - probability
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This note was uploaded on 08/23/2009 for the course IEE 1036 taught by Professor Cwliu during the Spring '06 term at National Chiao Tung University.

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Lecture 02-probability - 1036: Probability & Statistics...

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