AP* Statistics Tutorial: Random Variables
When the numerical value of a
variable
is determined by a chance event, that variable is called a
random variable.
Discrete vs. Continuous Random Variables
Random variables can be
discrete or
continuous.
- Discrete. Discrete random variables take on
integer values, usually the result of counting. Suppose, for
example, that we flip a coin and count the number of heads.
The number of heads results from a random process - flipping a coin.
And the number of heads is represented by an integer
value - a number
between 0 and plus infinity. Therefore, the number of heads
is a discrete random variable.
- Continuous. Continuous random variables, in
contrast, can take on any value within a range of values.
For example, suppose we flip a coin many times and
compute the average number of heads per flip.
The average number of heads per flip results from a random
process - flipping
a coin. And the average number of heads per flip
can take on any value between 0 and 1, even a
non-integer value. Therefore, the average number of heads
per flip is a continuous random variable.
Test Your Understanding of This Lesson
Problem 1
Which of the following is a discrete random variable?
I. The average height of a randomly selected group of boys.
II. The annual number of sweepstakes winners from New York City.
III. The number of presidential elections in the 20th century.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Solution
The correct answer is B. The annual number of sweepstakes winners
is an integer value and it results from a random process;
so it is a discrete random variable. The average height of a group
of boys could be a non-integer, so it is not a discrete variable.
And the number of presidential elections in the 20th century
is an integer, but it does
not vary and it does not result from a random process;
so it is not a random variable.
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