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Discrete Probability Distributions
Discrete Random Variables
Summary Measures
Continuous Probability Distributions
Statistical Sampling and Regression

PreMBA Analytical Methods
Discrete Probability Distributions: Introduction

Business is full of uncertainties. Will the price of this stock be up at end the trading day? Will this project be completed in a month? Will a particular person be hired to fill this executive position? Each of these uncertainties can be represented by a variable of as yet undetermined value, which is said to be random.

Random variables have values that are determined by chance events. The future price of a share of stock is a random variable because its value is determined by chance factors such as market conditions, the accomplishment of revenue targets by the company, interest rates, and so on. Likewise, both the completion date of a project and the person who will be hired to fill a position are random variables.

The frequency with which such uncertain events or variables occur over time is measured by probability. By understanding probability, business professionals can quantify variables in order to make the best decisions for their companies.

Random variables can be either discrete or continuous. A random variable is discrete if it can assume only a finite number of values or if its values are distinct and separate units. For example, the number of boxes of cookies produced during a given shift is a discrete random variable, because each box is a distinct, whole unit; a manufacturer would not produce or measure half a box of cookies. Therefore, the values that this discrete random variable could assume are distinct separate units.

Alternatively, continuous random variables can assume any range of values along a continuum. Consider boxes of cookies again. The weight of a box of cookies is a continuous random variable because it can be measured using an infinite range of fractional values. For example, the weight could assume values such as 16 ounces, 16.24 ounces, 16.2411 ounces, or any of a range of fractional values. Its value is not restricted to distinct units.

This section of the course will focus on discrete random variables. It begins by treating the essential rules of probability that apply to discrete random variables. Next is a review of of the probability distributions of discrete random variables, with an emphasis on binomial distributions, which are frequently used in quality-control inspections in manufacturing processes. The end of this section treats how the summary measures of expected value, variance, and standard deviation are applied to examples of discrete probability distributions.

When you have completed the Discrete Probability Distributions section of this course, you should be able to

  • describe the essential rules of probability and solve simple, business-related probability problems
  • differentiate between discrete and continuous variables and interpret discrete probability distributions
  • calculate the expected value, variance, and standard deviation of discrete probability distributions

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