Lecture series on probability and random variables by prof. Expectation, indicator random variables, linearity. Ex z all x xpx xdx this is a natural generalization of what we do when deciding if a casino game is fair. Random variable a realvalued function on the sample space example. Random variables and expectation relevant textbook passages. This course is a fastpaced course like many courses in the depart. Lecture 14 random variables ma 217 stephen sawin fair eld university august 8, 2017. Lecture notes on information theory preface \there is a whole book of readymade, long and convincing, lavishly composed telegrams for all occasions.
Jul 09, 2008 lecture series on probability and random variables by prof. Jagannatham of iit kanpur explains the following concepts in probability and random variables processes for wireless communications. Lecture notes ee230 probability and random variables department of electrical and electronics engineering middle east technical university metu preface these lecture notes were prepared with the purpose of helping the students to follow the lectures more easily and e ciently. The link is provided by the concept of a random variable. A random variable is said to be of continuous type if its distribution function is. In the second semester of the academic year 20112012 and for reasons unknown, i was asked to teach a course on probability and random processes to secondyear informatics students. Af t directly and check that it only depends on x t and not on x u. So far, we have seen several examples involving functions of random variables. First, if we are just interested in egx,y, we can use lotus. Lecture 4 random variables and discrete distributions. We discuss distributions, cumulative distribution functions cdfs, probability mass functions pmfs, and the hypergeometric distribution. Random variables, probability density function pdf. Probability and random variables processes for wireless communications video. Denition 3 the distribution function of a random variable x is the function.
So this is the random variable, and well often denote that by rv. Nptel video lectures, iit video lectures online, nptel youtube lectures, free video lectures. Binomial random variables, repeated trials and the socalled modern portfolio theory pdf 12. This function is called a random variableor stochastic variable or more precisely a.
On the other hand, books written for the engineering students tend to be fuzzy in their attempt to avoid subtle mathematical concepts. As a result, we always end up having to complement the. The function is called the probability density function p. Suppose we we want to know if 0 or not, where 0 is a speci c value of. Oct 28, 2015 page 1 nptel probability and distributions dept. Technically, a random variable must be ameasurable function. Given an random experiment, a random variable is a function or map from sample space to numbers. The probability density function describles the the probability distribution of a random variable. The random number generator will spread its output uniformly across the entire interval from 0 to 1 as we allow it to generate a long sequence of numbers. Mathematically, a random variable x is a realvalued function on. Lecture 4 introduction to random variables youtube. Chakraborty, department of electronics and electrical communication engineering, i.
Nptel online videos, courses iit video lectures well organized. Height weight number of males in a class types of random variables discrete are countable. Probability and statistics online course video lectures by. We use random variables to help us quantify the results of experiments for the purpose of analysis. Random variables, probability density function pdf youtube. A random variable is a variable whose value is a numerical outcome of a random phenomenon, so its values are determined by chance. When dealing with random variables, specifying the support is critical just as specifying the sample space is critical when conducting probability computations.
Descriptive statistics 2 lectures point estimation 2. The relationship between a random variable and its distribution can seem subtle but it is essential. We shall use letters such as x or y to represent a random variable, and x or y to represent a single outcome of the random variable. Define the probability density function and cumulative distribution function of a. We can think of a random event as a possible value that a random variable takes on. Its not a lecture or a course but one of the best ways to learn probability theory and random variables imo is from the two volume textbook introduction to probability theory and its applications by william feller.
Random variables types of rvs random variables a random variable is a numeric quantity whose value depends on the outcome of a random event we use a capital letter, like x, to denote a random variables the values of a random variable will be denoted with a lower case letter, in this case x for example, px x there are two types of random. Before data is collected, we regard observations as random variables x 1,x 2,x n this implies that until data is collected, any function statistic of the observations mean, sd, etc. Lecture 1 introduction to the theory of probability. I am releasing the pdf notes that are meant to accompany the nptel video course. Nptel provides elearning through online web and video courses various streams.
Lecture 1 introduction to the theory of probability youtube. A probability distribution tells us the possible values of a random variable, and the probability of having those values. The central limit theorem, distributions of the sample mean and the sample variance for a normal population, chisquare, t and f distributions, problems. For example, if we are ipping a coin, we may want to know if the coin is fair. How to download all of the lectures for a course in nptel quora. Random variables and probability distributions random variables suppose that to each point of a sample space we assign a number. Where can i find the best lectures on probability theory. See random variable r is a function r from the sample space to the reals.
Classical, relative frequency and axiomatic definitions of probability, addition rule and conditional probability, multiplication rule, total probability, bayes theorem and independence, problems. Somesh kumar,department of mathematics,iit kharagpur. The set of values that the random variable can take on is called its support. In this lecture, we will focus on the types of random variables. Nptel video lectures, iit video lectures online, nptel.
A random variable x on a sample space sis a function x. Recall a discrete probability distribution or pmf for a single r. In many situations, one is interested in only some aspects of the random experiment. Functions of two continuous random variables lotus. Jointly distributed random variables 1 lecture transformations of random vectors 1 lecture sampling distributions 2 lectures 7. A random event is something that may or may not occur, and that which we can assign a probability to. Theexpected value ex of a random variable x is the average value if we were to interpret the probabilities as frequencies. We then have a function defined on the sample space. R that assigns a real number xs to each sample point s 2s. When we have two continuous random variables gx,y, the ideas are still the same. Functions of a random variable 1 lecture jointly distributed random variables 3 lectures 6. Where can i find the best lectures on probability theory and. For continuous distributions, the probability density function has the following properties.
Find materials for this course in the pages linked. The results of many trials are represented by the density curve of a uniform distribution. If we are testing the e ect of two drugs whose means e ects are 1 and. Lecture notes ee230 probability and random variables. You see, what gets transmitted over the telegraph is not the text of the telegram, but simply the number under which it is listed in the book. In fact, a random variable is a function from the sample space to the real numbers. Find materials for this course in the pages linked along the left.
How to download all of the lectures for a course in nptel. Theorem 6 probability density function let x be a continuous random variable. Random variables a random variable is a number whose value depends upon the outcome of a random experiment. If you have the pf then you know the probability of observing any value of x. A random variable is a realvalued function on the sample space, s.
Lecture notes 10 hypothesis testing chapter 10 1 introduction let x 1x n. Freely browse and use ocw materials at your own pace. Functions of two continuous random variables lotus method. Sending such a telegram costs only twenty ve cents. Two types of random variables a discrete random variable has a countable number of. Probability and statistics probability and statistics. So numerical variables and random variables are two di erent ways to look at the same thing. The probability density function of a gaussian random variable is given by fxx 1.
You have given all information about a discrete random variable when you list the values and the probabilities, e. Then the probability density function pdf of x is a function fx such that for any two numbers a. Tech s4 lecture notes on ma204 probability distributions, random processes and numerical methods admin 20170425t17. So, you want to download all of the video lectures for a course in nptel. Questions from video lectures of nptel sl no questions video number time in minutes 1 give some examples for the communication systems which use space as the channel. Nptel provides elearning through online web and video courses various. Jan bouda fi mu lecture 2 random variables march 27, 2012 4 51. Its probability density function fx has the following properties, px x 0, pa. Every random variable has a distribution function, given by 1. Statistics 104 colin rundel lecture 8 february 8, 2012 5 24 chapter 3.