hich of the following variables would be an example of a discrete variable?
Student height
Student weight
Student's blood pressure
Year of birth of the student
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Answer:
Discrete and Continuous Random Variables
The word discrete means countable. For example, the number of students in a class is countable, or discrete. The value could be 2, 24, 34, or 135 students, but it cannot be 2332 or 12.23 students. The cost of a loaf of bread is also discrete; it could be $3.17, for example, where we are counting dollars and cents, but it cannot include fractions of a cent.
On the other hand, if we are measuring the tire pressure in an automobile, we are dealing with a continuous random variable. The air pressure can take values from 0 psi to some large amount that would cause the tire to burst. Another example is the height of your fellow students in your classroom. The values could be anywhere from, say, 4.5 feet to 7.2 feet. In general, quantities such as pressure, height, mass, weight, density, volume, temperature, and distance are examples of continuous random variables. Discrete random variables would usually come from counting, say, the number of chickens in a coop, the number of passing scores on an exam, or the number of voters who showed up to the polls.
Between any two values of a continuous random variable, there are an infinite number of other valid values. This is not the case for discrete random variables, because between any two discrete values, there is an integer number (0, 1, 2, ...) of valid values. Discrete random variables are considered countable values, since you could count a whole number of them. In this chapter, we will only describe and discuss discrete random variables and the aspects that make them important for the study of statistics.
Random Variables
In real life, most of our observations are in the form of numerical data that are the observed values of what are called random variables. In this chapter, we will study random variables and learn how to find probabilities of specific numerical outcomes.
The number of cars in a parking lot, the average daily rainfall in inches, the number of defective tires in a production line, and the weight in kilograms of an African elephant cub are all examples of quantitative variables.
If we let X represent a quantitative variable that can be measured or observed, then we will be interested in finding the numerical value of this quantitative variable. A random variable is a function that maps the elements of the sample space to a set of numbers.
Looking at Different Types of Random Variables
Three voters are asked whether they are in favor of building a charter school in a certain district. Each voter’s response is recorded as 'Yes (Y)' or 'No (N)'. What are the random variables that could be of interest in this experiment?
As you may notice, the simple events in this experiment are not numerical in nature, since each outcome is either a 'Yes' or a 'No'. However, one random variable of interest is the number of voters who are in favor of building the school.
The table below shows all the possible outcomes from a sample of three voters. Notice that we assigned 3 to the first simple event (3 'Yes' votes), 2 to the second (2 'Yes' votes), 1 to the third (1 'Yes' vote), and 0 to the fourth (0 'Yes' votes).