ChE253K Spring09 Lecture12.4 (1)

ChE253K Spring09 Lecture12.4 (1) - 1 ChE 253K Lecture 13...

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Unformatted text preview: 1 ChE 253K Lecture 13 Class Business Midterm 01 Mean: 177 StDev: 28 Answers posted Submit Qs by Friday Pick-up HW05 & MT01 HW06 due Monday, March 23 Please use the Cover Sheet 2 ChE 253K Lecture 13 Formulas & Axioms of Probability Addition P(A or B) = P(A) + P(B) Multiplication P(A and B) = P(A) P(B) Complement P(last) = 1 P(others) Interval 0 P(A) 1 Summation P(S) = 1 Union P(A B) = P(A)+P(B)P(A B) 3 ChE 253K Lecture 13 How To Describe And Use Probability Distributions Lecture 13 -- Inferential Statistics 4 ChE 253K Lecture 13 08Oct2007 Outline Of This Lecture Probability Distn Concepts Random variables Proby distn functions & examples Mean & std dev of distributions Some Useful Probability Distns Binomial Poisson Hypergeometric Geometric skim 5 ChE 253K Lecture 13 Readings Re: This Lecture Probability distns and their mean & std dev Chapter 4, Sect. 4.1 & 4.3 Bernoulli Trials and Binomial Distribution Chapter 4, Sect. 4.2 Poisson, Hypergeometric, Geometric Distns Sections 4.3, 4.7 & 4.8 6 ChE 253K Lecture 13 Experiment Random Variables Random Error X-Mean = X i 1-D Data Model = Random Variable Sources: liftlab.com/think/nova 7 ChE 253K Lecture 13 Probability is . Model-able Theoretical Experimental Subjective Modeling N(E) P(E) N(S) = 5 1 0 1 5 2 0 2 5 3 0 <9 11 15 19 21 27 31 In te rva l M id p o int Frequenc n = 32 8 16 24 32 Sources: www.penseur.org 8 ChE 253K Lecture 13 Probability is ... Program-able Sources: news.uns.purdue.edu www.satirworkshops.com Problem Type Known Distribution Probability 9 ChE 253K Lecture 13 Probability Distn Functions Probability that the measured value is x P(X = x) = f(x) The result of any particular measurement is unpredictable a random variable X, but the proportion of many that are x is f(x). Discrete or Continuous. Finite or Infinite. Probability Function Axioms of Probity f(x) 0 and f(x) = 1 10 ChE 253K Lecture 13 Simple Probability Functions Expt: Roll 1 Dice. Measure: Number Dots f(x) = 1/6 Expt: Roll 2 Dice Measure: Sum of Dots f(x) = x 1 2 3 4 5 6 f(x) 1/6 1/6 1/6 1/6 1/6 1/6 x 1 2 3 12 f(x) 0/36 1/36 2/36 1/36 11 ChE 253K Lecture 13 Point vs. Cumulative Probabilities Expt: Roll 1 Dice. Measure: Number Dots Interval Probability Function f(x) = 1/6 Cumulative Probability Function F(x) = x 1 2 3 4 5 6 f(x) 1/6 1/6 1/6 1/6 1/6 1/6 x 1 2 3 4 5 6 F(x) 1/6 2/6 3/6 4/6 5/6 6/6 12 ChE 253K Lecture 13 08Oct2007 ChE 253K Fall07 Lecture 11 Outline Of This Lecture Probability Distn Concepts Random variables Proby distn functions & examples Mean & std dev of distributions Some Useful Probability Distns Binomial Poisson Hypergeometric Geometric 13...
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ChE253K Spring09 Lecture12.4 (1) - 1 ChE 253K Lecture 13...

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