Although I cannot allow corrections for Test 3 (originally they were only supposed to be for Test 1!), there will be problems that require recognizing and computing special probabilities in Test 4 and on the Final Exam, and I can use them to possibly improve your scores on Test 4.

 

In order for this to happen, I need you to do the following:

• Scan or take a CLEAR, LEGIBLE photo of the last two pages of your Test 3. (I need to see the scoring.)

• Post the scan or photo to Piazza as a private note to me.

Note: scans are usually easier to read than photos. There is a pretty good scan app called Genius Scan. I posted instructions for using it on another blog. (You should make sure that the name your save your file under contains your name and Test 3.)

[Latexpage]

NOTE: there will be a quiz on Wednesday, based on one of the problems in Confidence Intervals listed below.

 

Please see this posts for notes: and also more notes and sources on the CLT here: (including yet another link to the resources explaining how to use your graphing calculator to compute special probabilities): Also make sure that you have done the homework in this post! (as usual)

• Additional practice on the exponential distribution and the Central Limit Theorem:
MAT2572additionalExponentialCLTproblems

The problems to do are marked with either a colored dot or a colored line in the margin, except you should omit #8.65(a) and 8.66(a). I will post the answers shortly. Please do these by next Monday at the latest.

• Problems on Confidence Intervals: in your textbook,

p. 309 # 5.3.1, 5.3.2, 5.3.3, 5.3.4, 5.3.13, 5.3.19

Note: in some of these, data is given and you will have to compute the sample mean from the data: just take the ordinary average of the data. Here is a way to enter the data and get the sample mean on TI calculator.  and here it is for the Casio graphing calculator.

MAT2572section5.3problems

• For practice identifying the various special discrete probability distributions, use these problems.  On first time through, just identify the special distribution (binomial, hypergeometric, poisson, negative binomial, geometric, etc.) and its parameters. Then check your answers against what is given in the last few pages. Testing yourself is one of the best learning methods. You can then go back and test yourself a few days later. Try not to memorize answers based on superficial features of the problem, but rather think about the problem and analyze it to see how it fits with its probability distribution. See these notes:

Math2501DistinguishSpecialProbabilityDistributions

• Please make sure that you have saved your scripts for simulations of the distributions in problems 3.3.1 and 3.3.2, based on the script I did in class and which is also included in this post. You do not have to submit them at this time: we will be using them in a few days to do some hypothesis testing (goodness-of-fit).

 

Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!

 

: answers to the extra practice problems

Math8.1practiceDiscretePartSolns

Please SKIP the following problems, which refer to distributions or theorems we have not discussed in this class: skip #8, 11, 14, 22, 25, 30, 33, 35, 38, 40

On first time through, just identify the special distribution (binomial, hypergeometric, poisson, negative binomial, geometric, etc.) and its parameters. Then check your answers against what is given in the last few pages. Testing yourself is one of the best learning methods. You can then go back and test yourself a few days later. Try not to memorize answers based on superficial features of the problem, but rather think about the problem and analyze it to see how it fits with its probability distribution. See these notes:

Math2501DistinguishSpecialProbabilityDistributions

Math2501-CentralLimitTheorem-slideshow

Math2501-CriticalValuesZ-slideshow

Math2501EstimationConfidenceIntervals

Math2501SamplingDistributionsEstimation

 

simulations example:

 

orbs <- c(1:5)

orb_samples <- replicate(10, sample(orbs, 2, replace = TRUE))

X <- apply(orb_samples, 2, max)

info <- hist(X, breaks = c(0.5, 1.5, 2.5, 3.5, 4.5, 5.5))

with(info, text(mids, counts, labels = counts, pos = 1))

#The below makes a relative frequency histogram

h <- hist(X, plot = FALSE)

h$counts <- h$counts/sum(h$counts)

plot(h, freq = TRUE, ylab = “Relative Frequency”)

 

Datacamp courses: suggestions for snow day makeup

General programming in R:

Intermediate R

Writing Functions in R

Data Visualization in R

 

Making Reports using R:

Reporting with R Markdown

 

Probability and Statistics:

Foundations of Probability in R (starting with Chapter 2)

Statistical Modeling in R (part 1)

 

Financial and Marketing Applications:

Bond Valuation and Analysis in R

Credit Risk Modeling in R

Equity Valuation in R

Financial Trading in R

Introduction to Portfolio Analysis in R

Introduction to R for Finance

Forecasting Product Demand in R

 

 

Also please make sure that you have done and checked the homework problems in this post.

• Problems from the textbook: special distributions (continued)

p. 262 #4.4.1, 4.4.3

p. 269 #4.5.1, 4.5.3

p. 274 #4.6.1, 4.6.2, 4.6.6 (challenge!), 4.6.7 (uses the value of gamma of 1/2 from 4.6.6, plus the recursion relation for the gamma function.)

• Problems from the textbook on the CLT:

p. 259 #4.3.33 (I did the first part in class)

Also please read this blog post (and view the video included), which has a very nice explanation of both the normal distribution and the central limit theorem using bunnies and dragons.

• Don’t forget to choose your Datacamp course for the snow day make up 

• Also don’t forget to do the Datacamp assignment on the binomial distribution (pay attention to how the simulation is done: your next programming assignments will be on simulating certain distributions.)