1st Tuesday of February! Warm-Up: Go on the Socrative app and answer the questions in Room: CHUNG (or share with someone and write in notebook) Quickwrite… Explain and give an example for each of your Warm-Up answers Ex: “I think I am more of an __________ because ________________. I think most teachers are __________ because _________________.”

Round Robin… starting with the student who spoke the most at your table today (1 min) Quickwrite… Explain and give an example for each of your Warm-Up answers Ex: “I think I am more of an __________ because ________________. I think most teachers are __________ because _________________.”

Personality Types

Random variables & probability distribution

Random Variables In most of the cases we will consider, a discrete random variable will be the result of a count Ex: The number of students in a statistics class is a discrete random variable (values such as 15, 25, 50, and 250 are all possible) However, 25.5 students is not a possible value for the number of students

Random Variables Most of the continuous random variables we will see will occur as the result of a measurement on a continuous scale Ex: the air pressure in an automobile tire represents a continuous random variable (the air pressure could, in theory, take on any value from 0 lb/in2 (psi) to the bursting pressure of the tire) Values such as 20.126 psi, 20.12678 psi, and so forth are possible

Example

What is a Probability Distribution? It is an assignment of probabilities to a random variable

Example: Discrete Probability Distribution Dr. Mendoza developed a test to measure boredom tolerance. He administered it to a group of 20,000 adults between the ages of 25 and 35. The possible scores were 0, 1, 2, 3, 4, 5, and 6, with 6 indicating the highest tolerance for boredom Boredom Tolerance Test Scores for 20,000 Subjects

Example: Discrete Probability Distribution If a subject is chosen at random from this group, the probability that he or she will have a score of 3 is 6000/20,000, or 0.30 In a similar way, we can use relative frequencies to compute the probabilities for the other scores Probability Distribution of Scores on Boredom Tolerance Test

Example: Discrete Probability Distribution The graph of this distribution is simply a relative-frequency histogram Graph of the Probability Distribution of Test Scores

Example: Discrete Probability Distribution The boringest Job Company needs to hire someone with a score on the boredom tolerance test of 5 or 6 to operate the Lamest Job Machine Since the scores 5 and 6 are mutually exclusive, the probability that someone in the group who took the boredom tolerance test made either a 5 or a 6 is the sum P(5 or 6) = P(5) + P(6) = 0.08 + 0.02 = 0.10 Probability Distribution of Scores on Boredom Tolerance Test