PPT-6.1: Discrete and Continuous Random Variables

Section 61 Discrete amp Continuous Random Variables After this section you should be able to APPLY the concept of discrete random variables to a variety of statistical settings CALCULATE and INTERPRET the mean expected value of a discrete random variable. QSCI 381 – Lecture 12. (Larson and Farber, Sect 4.1). Learning objectives. Become comfortable with variable definitions. Create and use probability distributions. Random Variables-I. A . 5.1 Discrete-time Fourier Transform . Representation for discrete-time signals. Chapters 3, 4, 5. Chap. 3 . Periodic. Fourier Series. Chap. 4 . Aperiodic . Fourier Transform . Chap. 5 . Aperiodic . Introductory Lecture. What is Discrete Mathematics?. Discrete mathematics is the part of mathematics devoted to the study of discrete (as opposed to continuous) objects.. Calculus deals with continuous objects and is not part of discrete mathematics. . 1. http://www.landers.co.uk/statistics-cartoons/. 5.1-5.2: Random Variables - Goals. Be able to define what a random variable is.. Be able to differentiate between discrete and continuous random variables.. http://. rchsbowman.wordpress.com/2009/11/29. /. statistics-notes-%E2%80%93-properties-of-normal-distribution-2/. Chapter 23: Probability Density Functions. http://. divisbyzero.com/2009/12/02. /. an-applet-illustrating-a-continuous-nowhere-differentiable-function//. 1. Matt Gormley. Lecture 2. August 31, 2016. School of Computer Science. Readings:. Mitchell Ch. 1, 2, 6.1 – 6.3. Murphy Ch. 2. Bishop Ch. 1 - 2. 10-601 Introduction to Machine Learning. Reminders. . .. . . Week 05 . Tues. . .. MAT135 Statistics. Random Variables. A random variable . . Random Variables. A random variable . . “varies” . . (not always the same). Random Variables. A random variable . Backus-Gilbert Theory. and. Radon’s Problem. Syllabus. Lecture 01 Describing Inverse Problems. Lecture 02 Probability and Measurement Error, Part 1. Lecture 03 Probability and Measurement Error, Part 2 . Chapter 5. Discrete-Time Process Models. Discrete-Time Transfer Functions. The input to the continuous-time system . G. (. s. ) is the signal:. The system response is given by the convolution integral:. Random variable: A variable whose value is determined by the outcome of a random experiment is called a random variable. Random variable is usually denoted by X. A random variable may be discrete or Nisheeth. Random Variables. 2. Informally, a random variable (. r.v.. ) . denotes possible outcomes of an event. Can be discrete (i.e., finite many possible outcomes) or continuous. Some examples of discrete . Consider. . the experiment of tossing a coin twice. . If we are interested in the number of heads that show on the top face, describe the sample space.. S. ={ HH , HT , TH , TT }. 2 1 1 0. Section 6.1. Discrete and Continuous. Random Variables. Discrete and Continuous Random Variables. USE the probability distribution of a discrete random variable to CALCULATE the probability of an event.. 1. http://www.landers.co.uk/statistics-cartoons/. 5.1-5.2: Random Variables - Goals. Be able to define what a random variable is.. Be able to differentiate between discrete and continuous random variables..