 Welcome to dealing with materials data, this course is on collection analysis and interpretation of materials data. We have completed two modules, first one was the introduction to R, the second one was descriptive statistics using R and in this module we are going to learn about probability distributions and how to use R to understand probability distributions and work with them. So this is the objective of this module. We want to understand probability distributions and their properties. The properties include density, distribution function and quantile function. We want to learn about common discrete probability distributions such as Bernoulli, Binomial, hypergeometric and Poisson for example and we want to learn about common continuous probability distributions like normal error function, log normal and Weibull for example. We want to learn about discrete and continuous uniform probability distribution. So uniform probability distribution can be either discrete or continuous. So we want to learn about uniform probability distribution because it plays a key role in some of the simulations that we have been carrying out and in order to understand what these simulations are it is important to understand uniform probability distribution. We will also learn about some common continuous probability distributions which are derived from normal such as chi-square, t and f distributions because these distributions are very useful in making parameter estimations are in understanding hypothesis testing. So they are of great use in hypothesis testing for example. So we will learn about them. We will also learn about gamma and beta probability distributions. So they have some use and relevance in inference. So we will learn about them. And from material science we do know that there are classical and quantum statistical distributions. Maxwell Boltzmann is a classical one, Fermi Dirac and Bose Einstein are the quantum statistical distributions. So we will have some exposure to them also in the same schema of things what are these distributions and how do they look and things like that we will learn. And we will also learn how to generate random variants from any of these distributions for doing computations and calculations. All of this we want to do using R and of course using materials data. So we will use materials data sets wherever possible or examples will be from materials wherever possible. And we will also discuss what is the expectation in terms of probability distributions when and why one should use normal, when and why one should use log normal and so on. So there are cases where we know a priori that the best distribution to describe the given data is variable for example or hyper geometric for example. So we will discuss some of these cases and so we will understand these issues better and also how to deal with them using R, how to work with these using R. And one more thing that we are going to do is that even though we are doing probability distribution now we have used some of these ideas in the previous module for example. So after going through this probability distribution session we are going to revisit some of the exercises to better understand what we did earlier. For example we have tried to fit the empirical data to some of the distributions. So after understanding these distributions we will go back and see what the fitting exercise was and what did we get and how do we understand those results a little bit better. So that is what we are going to do in this module. So this is the third module on probability distributions using R. Thank you.