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ChE253K Spring09 Lecture12.4 (1)

# ChE253K Spring09 Lecture12.4 (1) - Class Business Midterm...

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1 ChE 253K Lecture 13 Class Business Midterm 01 Mean: 177 StDev: 28 Answers posted Submit Q’s by Friday Pick-up HW05 & MT01 HW06 due Monday, March 23 Please use the Cover Sheet

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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

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4 ChE 253K Lecture 13 08Oct2007 Outline Of This Lecture Probability Dist’n Concepts Random variables Prob’y dist’n functions & examples Mean & std dev of distributions Some Useful Probability Dist’ns Binomial Poisson Hypergeometric Geometric skim
5 ChE 253K Lecture 13 Readings Re: This Lecture Probability dist’ns 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 Dist’ns Sections 4.3, 4.7 & 4.8

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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) = 0 5 10 15 20 25 30 <9 11 15 19 21 27 31 Interval Midpoint Frequenc n = 32 0 8 16 24 32 Sources: www.penseur.org

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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 Dist’n 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 Prob’ity f(x) 0 and Σ f(x) = 1

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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

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12 ChE 253K Lecture 13 08Oct2007 ChE 253K Fall07 Lecture 11 Outline Of This Lecture Probability Dist’n Concepts Random variables Prob’y dist’n functions & examples Mean & std dev of distributions Some Useful Probability Dist’ns Binomial Poisson Hypergeometric Geometric
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• Spring '08
• Staff
• Probability theory, Cumulative distribution function, ChE 253K Lecture, Binomial Poisson Hypergeometric Geometric

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