Distinguish between a discrete and continuous variable.
Answers
A variable is a quantity whose value changes.
A discrete variable is a variable whose value is obtained by counting.
Examples: number of students present
number of red marbles in a jar
number of heads when flipping three coins
students’ grade level
A continuous variable is a variable whose value is obtained by measuring.
Examples: height of students in class
weight of students in class
time it takes to get to school
distance traveled between classes
A random variable is a variable whose value is a numerical outcome of a random phenomenon.
▪ A random variable is denoted with a capital letter
▪ The probability distribution of a random variable X tells what the possible values of X are and how probabilities are assigned to those values
▪ A random variable can be discrete or continuous
A discrete random variable X has a countable number of possible values.
Example: Let X represent the sum of two dice.
Then the probability distribution of X is as follows:
X
2
3
4
5
6
7
8
9
10
11
12
P(X)
To graph the probability distribution of a discrete random variable, construct a probability histogram.
A continuous random variable X takes all values in a given interval of numbers.
▪ The probability distribution of a continuous random variable is shown by a density curve.
▪ The probability that X is between an interval of numbers is the area under the density curve between the interval endpoints
▪ The probability that a continuous random variable X is exactly equal to a number is zero