### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# INFO 1020 Week 1 Class Notes INFO 1020

DU

GPA 4.0

### View Full Document

## About this Document

## 50

## 1

## Popular in Analytics II: Statistics and Analysis

## Popular in Information System

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.

## Reviews for INFO 1020 Week 1 Class Notes

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

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

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.