ChE253K Lecture 19 -- MT2 Review.2

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

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
08Oct2007 2 ChE 253K Fall07 Lecture 11 How To Calculate Discrete Probabilities Lecture 12 -- Inferential Statistics
Background image of page 2
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 = =
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 6
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
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 8
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
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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)
Background image of page 10
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)
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 75

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

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online