discretion

Examples of discretion in the following topics:

• Probability Distributions for Discrete Random Variables

  • Probability distributions for discrete random variables can be displayed as a formula, in a table, or in a graph.
  • A discrete random variable $x$ has a countable number of possible values.
  • A discrete probability distribution can be described by a table, by a formula, or by a graph.
  • Sometimes, the discrete probability distribution is referred to as the probability mass function (pmf).
  • This histogram displays the probabilities of each of the three discrete random variables.

• Common Discrete Probability Distribution Functions

  • Some of the more common discrete probability functions are binomial, geometric, hypergeometric, and Poisson.

• Student Learning Outcomes

• Two Types of Random Variables

  • A random variable $x$, and its distribution, can be discrete or continuous.
  • Random variables can be classified as either discrete (that is, taking any of a specified list of exact values) or as continuous (taking any numerical value in an interval or collection of intervals).
  • Discrete random variables can take on either a finite or at most a countably infinite set of discrete values (for example, the integers).
  • Examples of discrete random variables include the values obtained from rolling a die and the grades received on a test out of 100.
  • This shows the probability mass function of a discrete probability distribution.

• Probability Distribution Function (PDF) for a Discrete Random Variable

  • This is a discrete PDF because

• Introduction

  • These two examples illustrate two different types of probability problems involving discrete random variables.
  • Recall that discrete data are data that you can count.
  • In this chapter, you will study probability problems involving discrete random distributions.

• Practice 1: Discrete Distribution

• The Discrete Fourier Transform

  • Suppose we have discrete data, not a continuous function.
  • This is the discrete version of the Fourier transform (DFT).
  • In the handout you will see some Mathematica code for computing and displaying discrete Fourier transforms.

• Expected Values of Discrete Random Variables

  • A discrete random variable $X$ has a countable number of possible values.
  • The probability distribution of a discrete random variable $X$ lists the values and their probabilities, such that $x_i$ has a probability of $p_i$.
  • The weights used in computing this average are probabilities in the case of a discrete random variable.

• Types of Variables

  • Numeric variables may be further described as either continuous or discrete.
  • A discrete variable is a numeric variable.
  • A discrete variable cannot take the value of a fraction between one value and the next closest value.
  • Variables can be numeric or categorial, being further broken down in continuous and discrete, and nominal and ordinal variables.
  • Distinguish between quantitative and categorical, continuous and discrete, and ordinal and nominal variables.