Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 Discrete Random Variable Examples: The number of students in a class The number of calls a salesperson makes in a day Continuous Random Variable 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.