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INFO 1020 Week 1 Class Notes

by: Alexandra Tilton

INFO 1020 Week 1 Class Notes INFO 1020

Marketplace > University of Denver > Information System > INFO 1020 > INFO 1020 Week 1 Class Notes
Alexandra Tilton
GPA 4.0

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Here are the notes from class on January 4 and January 6.
Analytics II: Statistics and Analysis
Ray Boersema
Class Notes
info, data, Analytics, analysis, Probability
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This 7 page Class Notes was uploaded by Alexandra Tilton on Thursday January 7, 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 50 views. For similar materials see Analytics II: Statistics and Analysis in Information System at University of Denver.

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Date Created: 01/07/16
INFO 1020:
 Analytics II Class Notes Mon. 1/04 Chapter 4: Introduction to Probability • Experiments • What is an experiment? • Definition: Any process which has a well-defined set of outcomes • Example T/F question: “An experiment is a process with a set of known outcomes and a set of unknown outcomes” • Example Experiment: Toss 3 coins and observe Heads or Tails • Sample Space: • Definition: Set of all possible outcomes • Probability • Definition: Anumber between and including 0 and 1. It indicates the frequency with which something happens. Can be expressed as a percent, fraction, or decimal • 3 Methods of Assigning Probability • Subjective: Personal opinion of the likelihood of something happening • Empirical: Doing an experiment repeatedly and counting outcomes to determine probability as observed results (rolling dice or tossing coins) • Classical: Mathematical and logical analysis !1 of !3 • Events • What do we mean by “event”? •Definition: Any subset of the sample space •Examples: A: exactly 3 heads = 1/8 B: penny is a heads = 4/8 C: nickel is a tails = 4/8 D: more than 1 head = 4/8 E: at most 2 heads = 7/8 •How do I calculate (Classical method) the probability of an event?: Classical probabilities are usually based on counting equally likely outcomes as listed versus performing an experiment (Empirical) •Law of Large Numbers: The more you do an experiment, the closer you get to the true probability • Complement • Definition: Denoted as A’ and is the event that contains outcomes not in A. P(A) + P(A’) = 1 • Example: P(E) = 7/8 therefore P(E’) = 1 - 7/8 = 1/8 • Union • Definition: Union of two events, B ∪ C, is the set of outcomes belonging to B OR C OR BOTH • Example: What is P(B ∪ C)? = 6/8 = P(B) + P(C) - P(B and C) • Intersection • Definition: The intersection of two events, B ∩ C, is the set of outcomes belonging to B AND C • Example: What is P(B ∩ C)? = 2/8 !2 of !3 • What is the Addition Law? •P(B) + P(C) - P(B and C) If events are mutually exclusive, how does the Addition Law • change? •There are no events in common • How does conditional probability differ from ordinary probability? •P(A| B) = 1/4: We’ve reduced sample space from 8 to 4. Sample space is usually reduced in cases of conditional probability •Example: What is P(A|C)? = 0 •Example: What is P(E|D)? = 0 • Frequency Table MARKETINMANAGEMENTACCOUNTINBIA FINANCE FRESHMAN 4 4 5 1 1 15 SOPHOMORE 2 4 1 6 2 15 JUNIOR 3 6 2 6 3 20 SENIOR 1 1 2 2 4 10 • If events are independent, then P(A| B) = P(A) •This is how you can prove events are independent !3 of !3 INFO 1020:
 Analytics II Class Notes Mon. 1/06 Chapter 5a: Discrete Probability Distributions • Random Variables: Discrete and Continuous • What is a random variable? • Definition: “x” whose value is a number which is dependent on the outcome of some experiment or observation • Example: Roll 2 dice • R.V. 1: Let x be the distance between the dice • R.V. 2: Let x be the sum of numbers on the tops • R.V. 3: Let x be the product of numbers on tops • R.V. 4: Let x be the time it takes to stop rolling • What makes a RV discrete? • Definition: x-values which are listable (R.V. 2 & R.V. 3). They do not have to be whole numbers. • What makes a RV continuous? • Definition: x-values which are un-listable (R.V. 1 & R.V. 4). They do not have to be whole numbers. • Examples: temperature, age, time, distance Page! of !4 • Discrete Probability Distributions • What is a probability function? • Definition: Aformula or a graph which provides all the x- values and associated P(x) - values • formula: P(x) = 1/2x Ɐ x ϵ {1,2,3,6} • table: x P(x) 1 1/2 2 1/4 3 1/6 6 1/12 • graph: x on x-axis and P(x) on y-axis • Can I list the required conditions for a Discrete Probability Function? • 3 Requirements: • 1: Every x-value • 2: Must have every P(x) - value 3: ΣP(x) = 1 • • Create a DPF: table and graph • Experiment: Roll two dice and multiply top two numbers • table x P(x) x P(x) x P(x) 1 1/36 9 1/36 24 2/36 2 2/36 10 2/36 25 1/36 3 2/36 12 4/36 30 2/36 4 3/36 15 2/36 36 1/36 5 2/36 16 1/36 6 4/36 18 2/36 8 2/36 20 2/36 Page ! of !4 • graph • How do I know if a DPF is uniform? • Definition: P(x) = k Ɐ x • Example: x P(x) 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6 • How do we calculate the expected value of a DRV? • To calculate expected value of x: E(x), the average x, #, = Σx⋅P(x) Page! of !4 • How do we calculate the VAR and STDEV of X? • To calculate variance (VAR): (x-E(x))² ⋅ P(x) • To calculate standard deviation: square root of variance Page! of !4


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