## here, you will find everything that you need for le cours

#### Week 1: Working with Data

Posted on August 20th, 2017

Updated on August 25th

Welcome to class, students. This week we will be getting our hands dirty touching and manipulating data of the easiest variety. The idea is to get us back to remembering certain mathematical notation and how to work with data.

There will be homework due EVERY Monday, including next Monday, August 28th, so please be sure to complete it and turn it in.

I am posting the lecture Handout for Quarter 1 here.

I am posting Homework for Quarter 1 here.

The problems from L1 and L2, from the homework handout, will be due on Monday, August 28th.

#### Week 2: Intro to Probability

Posted on August 31st, 2017

We have begun to dig into Probability: its basic properties, basic equations/rules/laws, and simple manipulation and definitions.

PLEASE, follow along in the book and stay on top of this material! We will be moving fast from here on out and you will need to be diligent with your study!

The problems from L3, L4, and L5, from the homework handout, will be due on Wednesday, September 6th, since Monday is Labor Day. Enjoy the long weekend, but please be safe!

#### Week 3:Probability Continued

Posted on September 7th, 2017

Monday: No Class, due to Labor Day

Wednesday: We began our short week with Lecture 6, treating the subject of independence. If I ask on a test if two random events are independent, you must be able to tell me yes/no with a justification.

Friday: We will begin to calculate Expectations of probability mass functions (pmf's), along with Variance and the like. This will all be on next week's exam on Friday, September 15th.

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You will have homework due on Monday, September 11th: L6 and L7 out of Edition 8 of the book. These two homeworks are very important for next week's first midterm, so please put a lot of energy into them.

I am posting the solutions to homeworks L1-l5 here for you to study. I will also post the solutions to L6/L7/L8 next week for you to study as well. We will NOT cover R until AFTER the midterm, and L8 will NOT be turned in. BUT you are responsible for the material including L8 on the midterm.

Here are the Solutions to L1 here.

Here are the Solutions to L2 here.

Here are the Solutions to L3 here.

Here are the Solutions to L4 here.

Here are the Solutions to L5 here.

#### Week 4:Probability Continued + first Midterm Exam

Posted on September 11th, 2017

Monday: Last day of new material before Friday's first Midterm exam. Binomial and Geometric Distributions were covered and YOU NEED TO KNOW THESE for the exam on Friday. Apart from doing the L8 homework, which I would get on as soon as possible (today, wink wink), the L10 review on Wednesday also covers these much needed topics for the exam: calculating expectations and binomial distribution.

Wednesday: This will be the exam review day, L10. You should try to go over this BEFORE Wednesday, so that you may have time to ask questions! You need to be able to complete all of L10 for the exam (beside the R programming part, but the concepts are all fair game).

Friday: Exam 1. Please, come prepared. Get some fresh air before taking the exam!

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I am posting the solutions to homeworks L6-l8 here for you to study. Recall: we will NOT cover R until AFTER the midterm, and L8 will NOT be turned in. BUT you are responsible for the material including L8 on the midterm (binomial distribution and expectation of a function of X).

Here are the Solutions to L6 here.

Here are the Solutions to L7 here.

Here are the Solutions to L8 here.

#### Week 5: Probability Distributions -- from Discrete to Continuous

Posted on September 20th, 2017

Updated on September 22nd, 2017

Monday: We finally got back to our L9 lecture, which introduced the Geometric and Poisson Distributions. Remember that these are discrete distributions. You should be able to tell me what they model: the Geometric is the first success in a sequence of Bernoulli trials (Binomial is the number of successes in a sequence of n Bernoulli trials) and the Poisson is the number of events that occur in a time period (we also saw space).

Wednesday: We started to rigorously define some properites of continuous distributions. These properties are analogous to the discrete distribution properties. Just keep in mind that a pdf and pmf are almost the same thing, they are just the function/curve of the distribution. The discrete function is a step function and we call it a probability mass function (pmf) and the continuous is a continuous function and we call it a probability density function (pdf) but we use them analosously (to find expectation, calculate probabilities, etc.).

I am posting the lecture Handout for Quarter 2 here.

I am posting Homework for Quarter 2 here.

The problems from L9, L11, and L12, from the two homework handouts, will be due on Monday, September 25th.

Friday: I am going to put the last example in the L12 handout: Washers2.

I also handed out the Exam 1, graded, this morning. For those who haven't picked it up, please come and do so.

There will be a curve, and the grades are as follows:

32 -- A

28 -- B+

22 -- B

18 -- C+

15 -- C

12 -- D

And you can find the Exam 1 Solutions, here.

#### Week 6: Probability Distributions cont...-- Continuous Distributions

Posted on September 26th, 2017

Monday: We talked about two new continuous probability distributions: the Normal (Gaussian) Distribution and the Exponential Distribution.

We will be using the Gaussian Distribution for MANY aspects of the rest of the class, so please begin to familiarize yourself with the properties of it, like the Z-score/standardization formula.

Wednesday: We began talking about joint distributions of random variables (rv's). This is a distribution that describes more than one rv through one functional form. As per the usual, the discrete and continuous versions have analogous mechanics (the way you calculate probabilities, marginals, and expectations).

Friday: We introduced the concepts of Covariance and Correlation. Since these concepts inherently describe properties between more than one variable, any types of questions dealing with these concepts require JOINT densities. Just go by the definition when calculating these!

Please, do the homework as early as possible this week to ensure you have time to ask questions and seek help!

Homework for L13, L14, and L15 are due on Monday, October 2nd.

#### Week 7: Applying the Concepts of Probability to Data: Statistics!

Posted on October 4th, 2017

Monday: We finished off Lecture 15 and reviewed the concepts of Joint Probability Distributions.

Wednesday: We begin to delve into the world of Statistics, looking at samples of random variables (i.e. data) and learning how to manipulate and -subsequently- interpret them.

I am posting the solutions to the previous homeworks, below, in important documents.

Here are the Solutions to L9 here.

Here are the Solutions to L11 here.

Here are the Solutions to L12 here.

Here are the Solutions to L13 here.

Here are the Solutions to L14 here.

Here are the Solutions to L15 here.

#### Week 8: The Central Limit Theorem (CLT) and Statistical Sampling + Exam 2

Posted on October 11th, 2017

Monday: We finished off Lecture 17 and reviewed the concepts of the CLT.

Wednesday: Today was a review for Exam 2, this Friday, October 13th. Please do a good job of preparing for this exam!

I am posting the solutions to the previous homeworks, below:

Here are the Solutions to L16 here.

Here are the Solutions to L17 here.

And this is the formula sheet that you will all be given.

#### Week 9: Interval Estimates -- Confidence Intervals

Posted on October 23rd, 2017

We spent all week talking about interval estimation: Confidence Intervals (CI).

The homework was L18 and L19. We will be skipping over L20 and L21.

I also handed out the Exam 2, graded. For those who haven't picked it up, please come and do so.

There will be a curve, and the grades are as follows:

30 -- A

26 -- B+

22 -- B

19 -- C+

15 -- C

10 -- D

And you can find the Exam 2 Solutions, here.

#### Week 10: Hypothesis Testing

Posted on October 23rd, 2017

This is the second week of the 3rd "Quarter" and we are beginning to discuss the age-old statistical concept of Hypothesis Testing. This is the fundamental context in modern science where we establish competing hypothesis and perform an experiment to validate our conjectured thoughts. We will see how this fits into a probabilistic framework and why it has been instrumental in changing the face of science throughout the 20th century.

The review handouts for the third Quarter of lectures can be found here.

The homework assignments for the third Quarter of lectures can be found here.

#### Week 11: Hypothesis Testing (cont...)

Posted on November 7th, 2017

This is the second week of Hypothesis Testing. Instead of estimating a single population mean or proportion, we are now delving into the world of multiple populations where we try to see if those populations are different from one another. We will first just compare 2 populations (think: are Boys taller than Girls, on average), and then extend into multiple populations.

#### Week 12: ANOVA + Exam 3

Posted on November 7th, 2017

Monday: We finished off Lecture 27 and briefly discussed the motivation of multiple comparisons after rejecting the null of an ANOVA test..

Wednesday: This will be a review for Exam 3, this Friday, November 10th. Please do a good job of preparing for this exam!

I am posting the solutions to the previous homeworks, below:

Confidence/Prediction Intervals

Here are the Solutions to L18 here.

Here are the Solutions to L19 here.

Hypothesis Tests: (single mean/proportion)

Here are the Solutions to L22 here.

Here are the Solutions to L23 here.

Here are the Solutions to L24 here.

Hypothesis Tests: (difference of mean/proportion)

Here are the Solutions to L25 here.

Here are the Solutions to L26 here.

ANOVA

Here are the Solutions to L27 here.

And here is the L28 solutions for you to look at:

Multiple Comparisons

the Solutions to L28 here.

And this is the formula sheet that you will all be given.

#### Week 13: Linear Regression

Posted on November 17th, 2017

This entire week was spent going over the basics of Simple Linear Regression.

We first needed to understand the concepts and properties and we will begin -after the Fall Break- to explore more powerful extensions of these concepts and models.

I am putting the Fall Break "Project" here as well as the email I sent.

The handouts and homeworks for the remaining lectures are found below with the important documents.

#### Week 14: Linear Regression cont...

Posted on December 1st, 2017

This entire week was spent delving into more topics relating to Linear Regression: inference on the coefficients, multiple regression, polynomial, residuals, and assumptions.

I am putting the Final "Project" here as well as the email I sent.

This project is due next Friday, December 8th, before 5pm.

The review worksheets are all found below. Remember, if you want to use them as replacements for homeworks they are due next Friday, December 8th before 5pm.

Week 1 Review Document: Descriptive Statistics Basics.

Week 2 Review Document: Probability

Week 3 Review Document: Discrete RVs

Week 4 Review Document: Continuous RVs (one more discrete problem)

Week 5 Review Document: CLT and Joint Distributions

Week 6 Review Document: Joint Distributions

Week 7 Review Document: Confidence Intervals for single parameters

Week 8 Review Document: Hypothesis tests for single parameters

Week 9 Review Document: Inference for differences in parameters

Week 10 Review Document: Regression

#### Week 15: Pre-Finals

Posted on December 8th, 2017

I am posting solutions to the last homeworks below:

Linear Regression

Here are the Solutions to L30 here.

Here are the Solutions to L31 here.

Here are the Solutions to L33 here.

Linear Regression (cont...)

Here are the Solutions to L34 here.

Here are the Solutions to L35 here.

Here are the Solutions to L36 here.

The solutions to the review worksheets are all found below.

Week 1 Review Document: Descriptive Statistics Basics.

Week 2 Review Document: Probability

Week 3 Review Document: Discrete RVs

Week 4 Review Document: Continuous RVs (one more discrete problem)

Week 5 Review Document: CLT and Joint Distributions

Week 6 Review Document: Joint Distributions

Week 7 Review Document: Confidence Intervals for single parameters

Week 8 Review Document: Hypothesis tests for single parameters

Week 9 Review Document: Inference for differences in parameters

Week 10 Review Document: Regression

#### This is where you will find all of our most important documents.

Updated on August 21st, 2017

Here is the course Syllabus.

Here is a short tutorial on the R programming language.

-----Homework/Handouts-----

-----Misc.-----

P-VALUES:

Here is the famous Z-table.

Here is the famous T-table.

This document explains how to find p-values on a TI-83.

This document explains how to find p-values on a TI-84.

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