ChE253K Lecture 19 -- MT2 Review.2

# ChE253K Lecture 19 -- MT2 Review.2 - Midterm#2...

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Midterm #2 Wednesday (April 8) in class Coverage: Lectures 12 - 18 and HW 6 - 10 References & Tools: Your calculator Four pages of notes #2 Pencils Scantron Required tables and hypo test procedure will be provided

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08Oct2007 2 ChE 253K Fall07 Lecture 11 How To Calculate Discrete Probabilities Lecture 12 -- Inferential Statistics
ChE 253K Spr08 Lecture 11 Probability is …. Theoretical Experimental “The probability of an event or outcome is the proportion of times the event occurs in a long run of repeated experiments.” Subjective Educated guesses based on experience N(E) Count of Outcomes in Event P(E) N(S) Count of Outcomes in Sample Space = =

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08Oct2007 ChE 253K Fall07 Lecture 11 Counting tools Inspection, experiment, etc Choice Multiplication (counting trees) Permutations (ordered) Combinations (unordered) ( 29 ( 29 ( 29 1 1 ! ! n r P n n n r n n r = - - + = - L ( 29 ( 29 ( 29 1 1 ! ! ! ! n r n n n n r n C r r r n r - - +   = = =   -   L ( ) ( ) ( ) N S N A N B = × × L
08Oct2007 ChE 253K Fall07 Lecture 11 Choice Multiplication Trees Prof Poehl drives to UT through 3 traffic lights. Each has two states: stop & go. What’s the size of the s&g state space? See also Text Fig 3.5 – beyond binary branches g s g s g s g s g s g s g s ggg ggs gsg

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08Oct2007 ChE 253K Fall07 Lecture 11 Permutations Permutation: An ordered arrangement of r objects selected from n distinct objects Number of arrangements of A, B, C, D, E ? × × × × = 5! ( 29 ( 29 ( 29 1 1 ! ! n r P n n n r n n r = - - + = - L 5 4 3 1 2 Sampling w/o replacement 5 of 5 r = n 0! = 1
08Oct2007 ChE 253K Fall07 Lecture 11 Permutation Example Given 10 students, 5 are to be chosen and lined up. How many different lines can be formed? ( 29 ( 29 1 1 10 9 8 7 6 30240 n r P n n n r = - - + = × × × × = L

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08Oct2007 ChE 253K Fall07 Lecture 11 Combinations Combination: An unordered group of r objects selected from n distinct objects What if the objects are not distinct? What if r (selects) equals n (pool) ? only 1 combination ( 29 ( 29 ( 29 1 1 ! ! ! ! n r n n n n r n C r r r n r - - +   = = =   -   L
08Oct2007 ChE 253K Fall07 Lecture 11 Combination Example Given 10 music students, a group of 5 is to be chosen. How many different groups can be formed? ( 29 ( 29 1 1 ! 10 9 8 7 6 30240 5! 30240 120 252 n r C n n n r r = - - + = × × × × = = = L

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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)
08Oct2007 ChE 253K Fall07 Lecture 11 Combining Probabilities Addition Rule The probability of occurrence of one of a group of mutually exclusive events is the sum of the probabilities the events. P(A or B) = P(A) + P(B) Multiplication Rule The probability of joint occurrence of two or more independent events is the product of their separate probabilities P(A and B) = P(A) × P(B)

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08Oct2007 ChE 253K Fall07 Lecture 11 Expectation Value If the probabilities of events A, B, C are P(A), P(B), P(C) and the “values” are V(A), V(B), V(C), then the expectation value <V> is: <E> = P(A) × V(A) + P(B) × V(B) + P(C) × V(C) Exp’t: Flip a dime Evnts: Heads you win. Tails you lose.
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ChE253K Lecture 19 -- MT2 Review.2 - Midterm#2...

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