The world around us is filled with uncertainty, risk, and variability that complicate day-to-day decisions and the development of long-term plans. This applies to personal decisions as well as decisions made by companies and government agencies. When you work on college applications, you cannot be sure which schools will accept you. In a rush to get a meal between classes, you will face uncertainty in the time it takes to be served at the school cafeteria. The school newspaper editor is concerned about how many members of the writing team will meet their deadlines. While reviewing alternative car insurance plans, the student driver struggles to decide on the size of the collision insurance deductible. Obviously, no one plans to have an accident, but the risk of an accident is always present. Companies that provide insurance look at the same problem. They come up with pricing strategies for insurance that pool the risk of an individual with large groups of similar people.
Variability is a characteristic of data that refers to the recognition that each data value is not the same. For example, there is variability in height of individuals or in their annual income. Two common statistics used to characterize a dataset’s variability are variance and standard deviation.
Companies launching a new product or service must deal with uncertain demand. Police patrol supervisors must consider random fluctuations in the demand for service and patterns of crime when planning how many patrol officers are needed on each shift and where to place them. Plant managers and school officials must cope with workers who randomly do not show up for work due to illness.
This text is designed to provide decision-making guidance in the presence of uncertainty. One of the challenges in learning basic concepts of probability is that many of us do not have good intuition about randomness. We will address this problem while developing probabilistic decision-making skills. The text is therefore designed to develop your ability to recognize and understand patterns of random events. We will do so by having you simulate random experiments first with a coin flip, then with the random number function in your calculator, and lastly, using the random number generator in Excel to develop and analyze a large sample.
In introducing basic concepts, we routinely use the concept of relative frequency as an estimate of probability. Thus, our introductory examples will use data rather than the counting methods that you may have seen in other probability courses.
Randomness is a characteristic of a process, experiment, or environment in which outcomes cannot be predicted with certainty. A random experiment, such as rolling a die, can yield different unpredictable outcomes. The gender of newborn is a result of a random process involved in becoming pregnant. The temperature on any day reflects randomness of our environment.
In later chapters we introduce mathematical formulas that can be used to describe different patterns of randomness. These are probability distributions. These formulas will be applied to two different types of variables: discrete and continuous. A discrete variable is countable. For example, the number of crimes in a day and the number of people absent from work are discrete variables. On the other hand, a continuous variable cannot be counted and is measured instead. For example, the time to complete an exam and the height of an individual are continuous variables.