Lecture 2

# Lecture 2 - Probability and Statistics in the Life Sciences...

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Probability and Statistics in the Life Sciences (Spring 2010) AMS 110.02 Chapter 3 Lecture 2 Donghyung Lee

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Before Studying Chapter 3 Probability First Quiz! Next Week. 1 or 2 problems! (30 minutes) It will be easy!! Don’t forget to bring your calculator. You’d better bring it every class. First HW! I posted it on our class website. It’s due date is Next Thursday (Feb. 11) and submit it before class start!!
Chapter 3 Read sections 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8. You don’t need to study section 3.9. Summary note for the probability theory and set theory will be given before the first midterm.

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Chapter 3 - Probability Definitions and Properties (1) Sample Space (S): The set of every possible outcomes of an experiment is called a sample space (S). Ex1) What is the sample space when you toss a coin S= {Head, Tail}={H,T} Ex2) What if you toss the coin twice? S= ? Ex3) What about rolling a die? S=?
Definitions and Properties (2) Event : an event is a subset of a sample space. Ex1) List all events of S={H,T}: {}, {H}, {T}, {H, T}. Ex2) # of all subsets of a set 2^(# of data in the set} For S={H,T} 2^2 = 4

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Definitions and Properties (3) Probability (p) (always between 0 and 1): a numerical quantity that expresses the likelihood of an event. The probability of an event E is written as P(E) or Pr(E). Ex1) Probability of a fair coin: S={H,T}. p({})=0 p({H})=1/2 P({T})=1/2 P({H,T})=1 Ex2) Probability of a fair die : S={1, 2, 3, 4, 5, 6}
Definitions and Properties (4-1) (Set Theory) Set operations - Union (or) (The set of all objects that are a member of A, or B, or both) - Intersection (and) (The set of all objects that are members of both) - Complement (not) (The set of all members of S that are not members of A) U I C { : } A B x x A or x B = U { : } A B x x A and x B = I { : } c A x x A =

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Definitions and Properties (4-2) (Set Theory) Let A and B be two events (S : Sample space) (a) (b) (c) (d) (e) ( ) ({}) 0 P P φ= = ( ) 1 ( ) c P A P A = - ( ) ( ) ( ) ( ) P A B P A P B P A B = + - I U ( ) 1 P S = , ( ) ( ) If A B P A P B ̣
Definitions and Properties (4-3) (Set Theory) Mutually exclusive If , then A and B are mutually exclusive. Independent

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## This note was uploaded on 03/28/2011 for the course AMS 110 taught by Professor N/a during the Spring '08 term at SUNY Stony Brook.

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Lecture 2 - Probability and Statistics in the Life Sciences...

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