Nptel online videos, courses iit video lectures well organized. Much of the advanced research in biology, genetics, and information. So this is the random variable, and well often denote that by rv. Some courses might have presentations or quiz papers uploaded, but rest of them just have transcripts which is pretty useless to refer as notes. Let, x be a random variable and is a function of a real variable a. Published by the oxford university press so it has jul 09, 2008 lecture series on probability and random variables by prof. Ex z all x xpx xdx this is a natural generalization of what we do when deciding if a casino game is fair. A random variable x on a sample space sis a function x.
Lecture series on probability and random variables by prof. On the other hand, books written for the engineering students tend to be fuzzy in their attempt to avoid subtle mathematical concepts. The probability function associated with it is said to be pdf probability density function pdf. If two random variables x and y have the same mean and variance. Lecture notes on probability theory and random processes. The core concept of the course is random variable i. Here you can download the free lecture notes of probability theory and stochastic processes pdf notes ptsp notes pdf materials with multiple file links to download. Probability theory and stochastic processes pdf notes sw. R,wheres is the sample space of the random experiment under consideration. It is true for any discipline, be it physical sciences, engineering and technology, economics or social sciences. In fact, a random variable is a function from the sample space to the real numbers.
Engineering analysisrandom variables wikibooks, open books. A random variable is a numerical description of the outcome of a statistical experiment. Random variables, probability density function pdf. Lecture 4 introduction to random variables youtube.
Lecture 4 random variables and discrete distributions. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Find materials for this course in the pages linked along the left. Probability and statistics probability and statistics. This function is called a random variableor stochastic variable or more precisely a. Tech students to know more about gate, gre, cat, gmat and many competitive exams and other stuffs. A random variable, x, is a function from the sample space s to the real. We will denote random variables by the abbreviation r. Jan bouda fi mu lecture 2 random variables march 27, 2012 4 51.
Chakraborty, does not currently have a detailed description and video lecture title. Somesh kumar,department of mathematics,iit kharagpur. Joint probability density function a joint probability density function for the continuous random variable x and y, denoted as fxyx. Pdf for productquotients of random variables find the probability density function for the ratio of the smallest to the largest sample among independent drawings from betadistribution 2, 3. Nptel video lectures, iit video lectures online, nptel youtube. For a continuous variable, the cumulative distribution function is written as. Applications of random discrete and continuous varibales 2. The properties of the random variable are known as the distribution of the random variable. Nptel electronics and communication engineering pdf. Random variables video lecture by prof somesh kumar of iit. If you have watched this lecture and know what it is about, particularly what engineering topics are discussed, please help us by commenting on this video with your suggested description and title. Chakraborty, department of electronics and electrical communication engineering, i.
Formula for determining the pdf of a random variable. Lecture 1 introduction to the theory of probability. We then have a function defined on the sample space. Bernoulli random variable a bernoulli random variable describes a trial with only two possible outcomes, one of which we will label a success and the other a failure and where the probability of a success is given by the parameter p. Majority of video courses on nptel do not offer lecture notes for download. R that assigns a real number xs to each sample point s 2s. Dec 03, 2019 pdf and cdf define a random variable completely. Random processes for engineers 1 university of illinois.
Random variables and probability distributions random variables suppose that to each point of a sample space we assign a number. Chapter 5 two random variables college of engineering. Aug 21, 2011 for the love of physics walter lewin may 16, 2011 duration. A random variable that may assume only a finite number or an infinite sequence of values is said to be discrete. Chapter 4 considers groups of random variables, with an emphasis on two random variables.
A random variable x is said to be continuous if it takes on infinite number of values. As it is the slope of a cdf, a pdf must always be positive. Gate preparation, nptel video lecture dvd, electronicsandcommunication engineering, probabilityand random processes, random variables, discrete random variables, continuous random variables, random variables, variables, generating functions, moment generating functions, generating functions moments, binomial, poisson, geometric, uniform, exponential, gamma distribution, normal. Bikash kumar dey department of electrical engineering iit bombay, powai mumbai 400 076, india.
A random variable can be interpreted as the result of a single measurement. Since it needs to be numeric the random variable takes the value 1 to indicate a success and 0 to indicate a. If two random variables x and y have the same pdf, then they will have the same cdf and therefore their mean and variance will be same. A random variable is a variable whose value is unknown, or a function that assigns values to each of an experiments outcomes. For example, let y denote the random variable whose value for any element of is the number of heads minus the number of tails. This course introduces you to the necessary sections of probability theory and statistics, guiding you from the very basics all way up to the level required for jump starting your ascent in data science. Random variables can be discrete, that is, taking any of a specified finite or countable list of values having a countable range, endowed with a probability mass function characteristic of the random variable s probability distribution. On the otherhand, mean and variance describes a random variable only partially. Fa px a fx dx a the probability that a continuous random variable takes on any value between. Classical, relative frequency and axiomatic definitions of probability, addition rule and conditional probability, multiplication rule, total probability, bayes theorem and independence, problems. Probability theory and stochastic processes pdf notes. This function is called a random variable or stochastic variable or more precisely a random function stochastic function. Probability and random processes random variables exam study.
See random variable r is a function r from the sample space to the reals. Exploration of data science requires certain background in probability and statistics. How to download notes directly in pdf format from nptel. Applications of random variable linkedin slideshare. Binomial random variables, repeated trials and the socalled modern portfolio theory. Probability and random processes random variables exam. Statistics random variables and probability distributions. Topics include describing the joint distribution of two random variables, covariance and correlation coe cient, and prediction or estimation of one random variable given observation of another. Introduction to probability theory and stochastic processes media storage type. Statistics 104 colin rundel lecture 8 february 8, 2012 5 24 chapter 3. Lectures from the national programme on technology enhanced learning mathematics probability and statistics. Probability and statistics nptel online videos, courses.
Probability, statistics, and random processes for electrical. Then, the expression leads to a new random variable y with the following connotation. The distribution of a single random variable is fairly simple to describe. Statistics statistics random variables and probability distributions.
Thus a pdf is also a function of a random variable, x, and its magnitude will be some indication of the relative likelihood of measuring a particular value. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields. It is completely speci ed by the cumulative distribution function fx, a function of one variable. Nptel video lectures, iit video lectures online, nptel youtube lectures. Probability theory and stochastic processes notes pdf ptsp pdf notes book starts with the topics definition of a random variable, conditions for a function to be a random. Joint, marginal and conditional distributions, product moments, correlation and regression, independence of random variables, bivariate normal distribution, problems. Freely browse and use ocw materials at your own pace. Binomial random variables, repeated trials and the socalled modern portfolio theory pdf 12.
If x is the random variable whose value for any element of is the number of heads obtained, then xhh 2. Gate preparation, nptel video lecture dvd, electronicsandcommunicationengineering, probabilityandrandomprocesses, randomvariables, discrete random variables, continuous random variables, random variables, variables, generating functions, moment generating functions, generating functions moments, binomial, poisson, geometric, uniform, exponential, gamma distribution, normal. Engineering analysisrandom variables wikibooks, open. Engineering example since pulloff force varies or exhibits variability, it is a random variable. Random variables, pdfs, and cdfs chemical engineering. Discrete let x be a discrete rv that takes on values in the set d and has a pmf fx. What is the best book to read about probability distributions. As a result, we always end up having to complement the. Define the probability density function and cumulative distribution function of a. Prepared by habib ur rehman chandio ce2k14001 dated. Probability and statistics video course course outline the use of statistical reasoning and methodology is indispensable in modern world. A random variable is a variable that takes a random value at any particular point t in time.