Statistics probability tutorial pdf

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If the events are mutually exclusive, there is no overlap: if one event occurs, other events cannot occur. In that case the probability of occurrence of one or another of more than one event is the sum of the probabilities of the separate events.

For example, if I throw a fair six-sided die the probability of any one face coming up is the same as the probability of any other face, or one-sixth. There is no overlap among these six possibilities. The Addition Rule corresponds to a logical or and gives a sum of separate probabilities. If the events are not mutually exclusive, there can be overlap between them. This can be visualized using a Venn diagram.

The probability of overlap must be subtracted from the sum of probabilities of the separate events. The circle marked A represents the probability or frequency of event A, the circle marked B represents the probability or frequency of event B, and the whole rectangle represents all possibilities, so a probability of one or the total frequency.

The set consisting of all possible outcomes of a particular experiment is called the sample space of that experiment. Thus, the rectangle on the Venn diagram corresponds to the sample space. An event, such as A or B, is any subset of a sample space. If the events being considered are not mutually exclusive, and so there may be overlap between them, the Addition Rule becomes —.

The overlap is the intersection between A and B. The basic idea for calculating the number of choices can be described as follows: Say there are n1 possible results from one operation.

For each one of these, there are n2 possible results from a second operation. In general, the numbers of possible results are given by products of the number of choices at each step. Probabilities can be found by taking ratios of possible results. The simplest form of the Multiplication Rule for probabilities is as follows: If the events are independent , then the occurrence of one event does not affect the probability of occurrence of another event.

In that case the probability of occurrence of more than one event together is the product of the probabilities of the separate events. Click on any of the links to grab your free copy of this highly recommended pdf:. Given below is the list of books recommended for the probability and statistics paper. Finding a reliable reference book online is no easy task. With the amount of information available, the guarantee of it being accurate, reliable and up to date is comparatively low.

This list of books is all verified by experts and recommend these books themselves. Also, these are recommended by teachers and students alike.

Having a reliable source of information will come in handy in your preparations. Most of the books recommended in this list are some of the only few books students can use for their preparations.

This list is in no particular order. It is advisable that if newer editions of these are available, students should opt for them because they will include any update in the syllabus and will also be the most up to date which will help you in your preparations a lot.

The entire syllabus of the syllabus covers a lot of ground. The field of probability and statistics is ever-growing with newer additions to this field thanks to the success in the research fields. Probability and statistics find its use in many fields, and therefore its applications are many and still counting.

Students when preparing for their exams should keep in mind that the entire syllabus is interconnected, so it does require constant effort from their side. The syllabus is divided into five units.

Each unit is a point of discussion in itself. Students should definitely look and make note that they are familiar with the topics and the understanding of the topic as well. Random variables — Discrete and continuous. Mathematical Expectation, Moment about the origin, Central moments Moment generating function of a probability distribution. Moment generating functions of the above three distributions, and hence finding the mean and variance. The covariance of two random variables, Correlation Coefficient of correlation, The rank correlation.

Sampling: Definitions of population, sampling, statistic, parameter. Types of sampling, Expected values of Sample mean and variance, sampling distribution, Standard error, the sampling distribution of mean and the sampling distribution of variance.

Student t-distribution, its properties; Test of significant difference between the sample mean and population mean; the difference between means of two small samples. Test of equality of two population variances.

Introduction to Stochastic Processes — Classification of Random processes, Methods of the description of random processes, Stationary and non-stationary random processes, Average values of single random processes and two or more random processes. The objective of the course is to familiarise the students with the important concepts of probability and statistics such as random variable, binomial and Poisson distribution, sampling, estimation, hypothesis, queuing and random processes.

Here is a list of some commonly asked theoretical problems of probability and statistics. Students can be asked to answer them in their exam papers and also during interviews. Keep in mind that these are basic entry-level questions to give you a better sense of the subject and what pattern does the examination paper follow-. Answer: Probability is the study of the possibility of any event in a random experiment. We calculate the probability to determine the possibility that an event occurs or not.

Equally likely events — These are events which have a similar probability of occurring. For example, during a coin toss, the probability of heads or tails is equal, i. Complementary events — Events which are opposite of each other.

Example of a complimentary event is will it rain or not tomorrow. Madhu Bhatia. Megha Aggarwal. Mike West. Michael Miller. Abhilash Nelson. Statistics - Probability Advertisements. Previous Page.