- MAS113 Introduction to Probability and Statistics
- Applications of conditional probability
- Probability: With Applications and R - AbeBooks - Dobrow, Robert P.:
- Learn more about Probability Theory

Each week students will also attend one tutorial, where they will work through set exercises.

Areas of common difficulty may be explained on the board by the tutorial leader. Students will also submit homework for marking but these will not count towards the assessment.

### MAS113 Introduction to Probability and Statistics

Introduction Statistical and probabilistic modelling, and the need for a mathematical theory of chance. Basic Probability Sets, unions, intersection, complement. Venn diagrams. Sample spaces and events. The idea of measure of a set. Counting measure.

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Properties of measures. Probability as measure. Calculating probabilities in practice - use of symmetry, relative frequencies, subjective probability. Joint and conditional probability, Bayes theorem, prior and posterior probabilities. Discrete Random Variables Discrete random variables. Expectation and variance and their properties e. Bernoulli, binomial, Poisson and geometric random variables. Calculations of laws, means and variances. The Poisson distribution as the limit of a binomial.

The binomial and Poisson distribution in R. Multivariate discrete random variables. Like this document? Why not share! Embed Size px.

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Start on. Show related SlideShares at end. WordPress Shortcode. Chiquitare Follow. Published in: Education. Full Name Comment goes here. Are you sure you want to Yes No. Be the first to like this. No Downloads. Views Total views. Actions Shares. Embeds 0 No embeds. RStudio can downloaded from the following link:. There are many reasons to use R. The fact that is a free and open-source software does not necessarily imply that it is a good software although it is also that. The reason why this is an important feature consists in the fact that the results of any code or program developed in the R environment can easily be replicated therefore ensuring accessibility and transparency for the general user.

More importantly however, this replicability of results is also accompanied by a wide variety of packages that are made available through the R environment in which users can find a diversity of codes, functions, and features that are designed to tackle a large amount of programming and analytical tasks. Moreover, new packages are relatively simple to create and are extremely useful for code-sharing purposes since they enclose the codes, functions, and external dependencies that allow anyone to easily and efficiently install these features. Additionally, these accessibility and code-sharing features have established R as a platform for development and dissemination of cutting-edge tools directly from the developer to the end-user.

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## Applications of conditional probability

RStudio is a customizable IDE for the R enviornment where the user can have easy access to plots, data, help, files, objects and many other features that are useful to work efficiently with R. For the most part, RStudio provides nearly everything the R user will need in a self-contained, and well-organized environment. Some examples of these tools are Rmarkdown which can be used respectively to integrate written narrative with embedded R code and other content, as well as and Shiny Web Apps which can provide an interactive user-friendly interface that permits a user to actively engage with a wide variety of tools built in R without the need to encounter raw R code.

GitHub and Rmarkdown will be the object of a more in-depth description in the first chapters of this book in order to provide the reader with the version-control and annotation tools that can be useful for the following chapters of this book. Throughout this book, R code will be typeset using a monospace font which is syntax highlighted.

For example:. Similarly, R output lines that usally appear in your Console will begin with and will not be syntax highlighted. The output of the above example is the following:. Therefore the following boxes and symbols can be used to represent information of different nature:. In the previous section we presented some examples on how R can be used as a calculator and we have already seen several functions such as sqrt or log.

For example, if you are interested in learning about the function log you could simply type:. The R documentation is written by the author of the package.

## Probability: With Applications and R - AbeBooks - Dobrow, Robert P.:

For mainstream packages in widespread use, the documentation is almost always quite good, but in some cases it can be quite technical, difficult to interpret, and possibly incomplete. In these cases, the best solution to understand a function is to search for help on any search engine. R comes with a number of built-in functions but one of its main strengths is that there is a large number of packages on an ever-increasing range of subjects available for you to install.

These packages provide additional functions, features and data to the R environement.

### Learn more about Probability Theory

If you want to do something in R that is not available by default, there is a good chance that there are packages that will respond to your needs. In this case, an appropriate way to find a package in R is to use the search option in the CRAN repository which is the official network of file-transfer protocols and web-servers that store updated versions of code and documentation for R see CRAN website.

R packages can be installed in various ways but the most widely used approach is through the install. The install. It is noteworthy that this approach assumes that the desired package s are available within the CRAN repository. This is very often the case, but there is a growing number of packages that are under-development or completed and are made available through other repositories. Sticking momentarily to the packages available in the CRAN repository, the use of the install. For example, if you want to install the package devtools you can simply write:.

Once a package is installed it is not directly usable within your R session. For example, after having installed the devtools package, in order to use it within your session you would write:.

Once this is done, all the functions and documentation of this package are available and can be used within your current session. However, once you close your R session, all loaded packages will be closed and you will have to load them again if you want to use them in a new R session. One of the main packages that is required for this class would be our STAT package, that contains all the necessary packages and functions that will be utilized in this book.

Run the following code to install the package directly from GitHub. There are many more elements in RStudio, and we encourage you to use the RStudio Cheatsheet as a reference. The R environment provides an up-to-date and efficient programming language to develop different tools and applications.