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## INFO 1020 Week 2 Class Notes

by: Alexandra Tilton

27

1

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# INFO 1020 Week 2 Class Notes INFO 1020

Marketplace > University of Denver > Information System > INFO 1020 > INFO 1020 Week 2 Class Notes
Alexandra Tilton
DU
GPA 4.0

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Here are the class notes for week 2, covering chapters 5 and 6!
COURSE
Analytics II: Statistics and Analysis
PROF.
Ray Boersema
TYPE
Class Notes
PAGES
12
WORDS
CONCEPTS
data, analysis, Analytics, information, Probability, distributions
KARMA
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## Popular in Information System

This 12 page Class Notes was uploaded by Alexandra Tilton on Thursday January 14, 2016. The Class Notes belongs to INFO 1020 at University of Denver taught by Ray Boersema in Winter 2016. Since its upload, it has received 27 views. For similar materials see Analytics II: Statistics and Analysis in Information System at University of Denver.

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Date Created: 01/14/16
INFO 1020:  Analytics II Class Notes Mon. 1/11 Chapter 5 Cont. • Word Problems • Types of Problems • General: P(x)s are different •Formulas: •ΣP(x) = 1 •E(x) = ▯ •VAR(x) = σ² = Σ(x-E(x))² ⋅ P(x) STDEV(x) = σ = Sqrt (Σ(x-E(x))² ⋅ P(x)) • • Uniform: All P(x)s are the same • Binomial Probability Distributions • Properties •Binomial Trial: Any trial that has just two outcomes •The trial is repeated n times •Trials are independent •Two trial outcomes: success and failure •Probability of success, p, is constant for each trial •The random variable, x, is the total possible number of successes •x ϵ [0,n] • Example: •Let the trial be toss a die •Let n = 4 Let success be “1” • Page▯ of ▯6 •Let failure be “not 1” •p = 1/6 •Probability Distribution (List the Xs and the P(X)) • Probabilities formula: P(x) = nCx (p^x) (1-p)^n-x • On calculator: Math, Probability, Combination • Example: P(3) = 4C3 (1/6)^3 (5/6)^1 = 0.0153 •Probability via Excel • =BINOM.DIST(x,n,p,0) •Shortcuts to means and variances • E(x) = ▯ = np = 4(1/6) = .667 • VAR(x) = σ² = np(1-p) = 4(1/6)(5/6) = .5556 • STDEV(x) = σ = sqrt (np(1-p) = 4(1/6)(5/6)) = .74 • Poisson Probability Distributions • Properties •Some events exist •Atime period exists The random variable, x, is the number of possible events • that occur during a given time period •E(x) = ▯ is given •x ϵ [o, ∞] • Example: •Observation: Event: Student coughs •Time period: one minute •x will be the number of coughs from 11:25 to 11:26 •E(x) = ▯ = 5 (this is given to us) •Calculate probability of 3 coughs • Probability formula: (▯^x)(e^-▯)/x! •Probability via Excel • =POISSON.DIST(x,mean,0) •IF PROBABILITY (P(X)) IS LESS THAN .001, STOP TABLE Page▯ of ▯6 • If you get a problem that asks what the probability of getting something greater than the probability you stopped at, then add up all until that number and subtract from 1. • Shortcuts to means and variances • E(x) = ▯ = given • VAR(x) = σ² = same as E(x) • STDEV(x) = σ = sqrt (E(x)) • Hypergeometric Probability Distributions • Properties • Apopulation of size N (N objects) • There is a subset of the population and its size is r. These could be called successes • Trial = pick n objects from the pot • The random variable, x, is the number of successes • x ϵ [0,n] The random variable, x, is the total possible number of • successes • x ϵ [0,n] or x ϵ [0(whichever is smaller) •Example: • N = 52 (cards) • r = 12 (faces) • n = 5 • x = # of face cards drawn • Probabilities formula: P(x) = (rCx) (N-rCn-x) (NCn) • On calculator: Math, Probability, Combination • Example: P(3) = 4C3 (1/6)^3 (5/6)^1 = 0.0153 • Probability via Excel • =HYPGEOM.DIST(x,n,r,N,0) • Shortcuts to means and variances • ***p = r/n (12/52) Page▯ of ▯6 • E(x) = ▯ = np • VAR(x) = σ² = np(1-p) • STDEV(x) = σ = sqrt (np(1-p) = 4(1/6)(5/6)) = .74 INFO 1020:  Analytics II Class Notes Mon. 1/13 Chapter 6 • Properties of all Continuous Probability Distributions • a: x ϵ : Real numbers • not listable • b: There may or may not be a smallest x, there may be a largest x • c: There is a probability function • d: The area under the graph is 1 • e: Areas are probabilities • f: P(x a particular number) = 0 • g: All probabilities will be for intervals of x-values • inclusive doesn’t make a difference • Properties of Uniform Continuous Probability Distributions • a: There IS a smallest x-value “a” There IS a largest x-value “b” • • b: y=f(x)=k (constant) • Straight line from “a” to “b” • Length of box (on graph) = “b”-“a” • Hight of box = 1/(“b”-“a”) Page▯ of ▯6 • c: P(c<x<d) = box within box = length*width •Area is (d-c)(1/b-a) • Example: Let x be time •Let a = 0 •Let b = 58 •P(X>40) = (18)(1/58) = 18/58 40 0 58 a b • d: The E(x) = ▯ = a+b/2 • e: The VAR(x) = σ² = (b-a)²/12 • f: σ = Square root of the VAR(x) • Properties of Standard Normal Continuous Probability Distributions • a: The random variable is z (not x) • b: No smallest z value (negative inﬁnity) No highest z value (positive inﬁnity) • • c: E(z) = 0 • d: STDEV(z) = 1 • e: y=f(x) is bell-shaped, goes from -3 to +3 • f: y=f(x)=(1/square root of (2pi))e^(-x²/2) = probability curve • g: Remember the Empirical Rule (.68), (.9544), (.9973) • EXCEL: =NORM.S.DIST(1,1) •P(Z<1.72): =NORM.S.DIST(1.72,1) •P(Z>1.72): =1-NORM.S.DIST(1.72,1) •P(-1.6<z<1.8): =NORM.S.DIST(1.8,1) - =NORM.S.DIST(-1.6,1) • h: To ﬁnd a cut point (z-value) =NORM.S.INV(area to the left) (subtract from one if you’re given it the other way around Pag▯ of ▯6 • Properties of Normal Continuous Probability Distributions • a: The random variable is x • b: No smallest x value •No largest x value • c: The E(x) = ▯ = given • d: σ = Square root of the VAR(x) = given • e: y=f(x) is bell-shaped, goes from ▯-3σ to ▯+3σ • EXCEL: =NORM.DIST(x value, mean, stdev,1) •Subtract from one if you need greater than (to the right) •Subtraction from two points if you need between •CUT POINT =Norm.INV(area to the left, mean, stdev) Page▯ of ▯6 INFO 1020:  Analytics II Class Notes Mon. 1/11 Chapter 5 Cont. • Word Problems • Types of Problems • General: P(x)s are different •Formulas: •ΣP(x) = 1 •E(x) = ▯ •VAR(x) = σ² = Σ(x-E(x))² ⋅ P(x) STDEV(x) = σ = Sqrt (Σ(x-E(x))² ⋅ P(x)) • • Uniform: All P(x)s are the same • Binomial Probability Distributions • Properties •Binomial Trial: Any trial that has just two outcomes •The trial is repeated n times •Trials are independent •Two trial outcomes: success and failure •Probability of success, p, is constant for each trial •The random variable, x, is the total possible number of successes •x ϵ [0,n] • Example: •Let the trial be toss a die •Let n = 4 Let success be “1” • Page▯ of ▯6 •Let failure be “not 1” •p = 1/6 •Probability Distribution (List the Xs and the P(X)) • Probabilities formula: P(x) = nCx (p^x) (1-p)^n-x • On calculator: Math, Probability, Combination • Example: P(3) = 4C3 (1/6)^3 (5/6)^1 = 0.0153 •Probability via Excel • =BINOM.DIST(x,n,p,0) •Shortcuts to means and variances • E(x) = ▯ = np = 4(1/6) = .667 • VAR(x) = σ² = np(1-p) = 4(1/6)(5/6) = .5556 • STDEV(x) = σ = sqrt (np(1-p) = 4(1/6)(5/6)) = .74 • Poisson Probability Distributions • Properties •Some events exist •Atime period exists The random variable, x, is the number of possible events • that occur during a given time period •E(x) = ▯ is given •x ϵ [o, ∞] • Example: •Observation: Event: Student coughs •Time period: one minute •x will be the number of coughs from 11:25 to 11:26 •E(x) = ▯ = 5 (this is given to us) •Calculate probability of 3 coughs • Probability formula: (▯^x)(e^-▯)/x! •Probability via Excel • =POISSON.DIST(x,mean,0) •IF PROBABILITY (P(X)) IS LESS THAN .001, STOP TABLE Page▯ of ▯6 • If you get a problem that asks what the probability of getting something greater than the probability you stopped at, then add up all until that number and subtract from 1. • Shortcuts to means and variances • E(x) = ▯ = given • VAR(x) = σ² = same as E(x) • STDEV(x) = σ = sqrt (E(x)) • Hypergeometric Probability Distributions • Properties • Apopulation of size N (N objects) • There is a subset of the population and its size is r. These could be called successes • Trial = pick n objects from the pot • The random variable, x, is the number of successes • x ϵ [0,n] The random variable, x, is the total possible number of • successes • x ϵ [0,n] or x ϵ [0(whichever is smaller) •Example: • N = 52 (cards) • r = 12 (faces) • n = 5 • x = # of face cards drawn • Probabilities formula: P(x) = (rCx) (N-rCn-x) (NCn) • On calculator: Math, Probability, Combination • Example: P(3) = 4C3 (1/6)^3 (5/6)^1 = 0.0153 • Probability via Excel • =HYPGEOM.DIST(x,n,r,N,0) • Shortcuts to means and variances • ***p = r/n (12/52) Page▯ of ▯6 • E(x) = ▯ = np • VAR(x) = σ² = np(1-p) • STDEV(x) = σ = sqrt (np(1-p) = 4(1/6)(5/6)) = .74 INFO 1020:  Analytics II Class Notes Mon. 1/13 Chapter 6 • Properties of all Continuous Probability Distributions • a: x ϵ : Real numbers • not listable • b: There may or may not be a smallest x, there may be a largest x • c: There is a probability function • d: The area under the graph is 1 • e: Areas are probabilities • f: P(x a particular number) = 0 • g: All probabilities will be for intervals of x-values • inclusive doesn’t make a difference • Properties of Uniform Continuous Probability Distributions • a: There IS a smallest x-value “a” There IS a largest x-value “b” • • b: y=f(x)=k (constant) • Straight line from “a” to “b” • Length of box (on graph) = “b”-“a” • Hight of box = 1/(“b”-“a”) Page▯ of ▯6 • c: P(c<x<d) = box within box = length*width •Area is (d-c)(1/b-a) • Example: Let x be time •Let a = 0 •Let b = 58 •P(X>40) = (18)(1/58) = 18/58 40 0 58 a b • d: The E(x) = ▯ = a+b/2 • e: The VAR(x) = σ² = (b-a)²/12 • f: σ = Square root of the VAR(x) • Properties of Standard Normal Continuous Probability Distributions • a: The random variable is z (not x) • b: No smallest z value (negative inﬁnity) No highest z value (positive inﬁnity) • • c: E(z) = 0 • d: STDEV(z) = 1 • e: y=f(x) is bell-shaped, goes from -3 to +3 • f: y=f(x)=(1/square root of (2pi))e^(-x²/2) = probability curve • g: Remember the Empirical Rule (.68), (.9544), (.9973) • EXCEL: =NORM.S.DIST(1,1) •P(Z<1.72): =NORM.S.DIST(1.72,1) •P(Z>1.72): =1-NORM.S.DIST(1.72,1) •P(-1.6<z<1.8): =NORM.S.DIST(1.8,1) - =NORM.S.DIST(-1.6,1) • h: To ﬁnd a cut point (z-value) =NORM.S.INV(area to the left) (subtract from one if you’re given it the other way around Pag▯ of ▯6 • Properties of Normal Continuous Probability Distributions • a: The random variable is x • b: No smallest x value •No largest x value • c: The E(x) = ▯ = given • d: σ = Square root of the VAR(x) = given • e: y=f(x) is bell-shaped, goes from ▯-3σ to ▯+3σ • EXCEL: =NORM.DIST(x value, mean, stdev,1) •Subtract from one if you need greater than (to the right) •Subtraction from two points if you need between •CUT POINT =Norm.INV(area to the left, mean, stdev) Page▯ of ▯6

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