Download 4.1AB: Random Variables and Probability Distributions Objectives: 1

4.1AB: Random Variables and Probability Distributions
Objectives:
1. To distinguish between discrete random variables and continuous random variables.
2. To construct a discrete probability distribution and its graph.
3. To determine if a distribution is a probability distribution.
Random Variable, x
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Discrete Random Variable
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 Examples:
 The number of students in a class
 The number of calls a salesperson makes in a day
Continuous Random Variable
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 Examples:
 The time it takes to run a mile
 The time spent on phone calls during a given day
Examples: Determine if each random variable is Discrete or Continuous
1. The amount of water in a 32 ounce container
2. The number of songs played by a band
3. The length of time it takes to complete a test
4. The height of a tree at a nursery
5. The number of suitcases lost by an airline
6. The number of skittles in a bag
7. The weight of newborn babies
Discrete Probability Distribution
 Lists each possible value the variable can be and its corresponding Probability
 Must satisfy each of the following conditions
1.
2.
Examples:
Determine if each is a Discrete Probability Distribution. Explain why or why not.
1.
2.
3. Find the missing value in the probability distribution:
Constructing a DISCRETE Probability Distribution
1. Make a Frequency Distribution for the possible outcomes
2. Find the Sum of the frequencies
3. Find the probability of each possible outcome
 Divide the Frequency of each by the sum of the frequencies
4. Check that each probability is between 0 and 1, inclusive, and that the sum is 1.
Example 1 Construct a Discrete Probability Distribution
An industrial psychologist administered a personality inventory test for passive-aggressive traits to 150 employees.
Individuals were given a score from 1 to 5, where 1 was extremely passive and 5 was extremely aggressive. A score
of 3 indicated neither trait. The frequency is shown below.
X
P(X)
Example 2 Construct a Discrete Probability Distribution
A company tracks the number of sales new employees make each day during a 100-day probationary period.
The results for one new employee are shown in the table below.