Week 1 - Lesson 4.1 Two Types Of Random Variable Flashcards
The word ____ 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 232 2 or 12.23 students. The cost of a loaf of bread is also _____; it could be $3.17, for example, where we are counting dollars and cents, but it cannot include fractions of a cent.
Discrete
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
Continous random variable
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.
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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.
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In real life, most of our observations are in the form of numerical data that are the observed values of what are called
Random variable
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 variable
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.
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Example: 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 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).
Table 4.1 on module
In the light of this example, what do we mean by random variable? The adjective ’random’ means that the experiment
may result in one of several possible values of the variable. For example, if the experiment is to count the number
of customers who use the drive-up window in a fast-food restaurant between the hours of 8 AM and 11 AM, the
random variable here is the number of customers who drive up within this time interval. This number varies from
day to day, depending on random phenomena, such as today’s weather, among other things. Thus, we say that the
possible values of this random variable range from 0 to the maximum number that the restaurant can handle.
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There are two types of random variablesdiscrete and continuous. Random variables that can assume only a
countable number of values are called discrete. Random variables that can take on any of the countless number
of values in an interval are called continuous
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The following are examples of
• The number of cars sold by a car dealer in one month
• The number of students who were protesting the tuition increase last semester
• The number of applicants who have applied for a vacant position at a company
• The number of typographical errors in a rough draft of a book
Discrete random variable
For each of these, if the variable is X, then x = 0,1,2,3,…. Note that X can become very large. (In statistics, when
we are talking about the random variable itself, we write the variable in uppercase, and when we are talking about
the values of the random variable, we write the variable in lowercase.)
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The following are examples of
• The length of time it takes a truck driver to go from New York City to Miami
• The depth of drilling to find oil
• The weight of a truck in a truck-weighing station
• The amount of water in a 12-ounce bottle
Continous random variable
For each of these, if the variable is X, then x > 0 and less than some maximum value possible, but it can take on any
value within this range.
Continous random variable
