Statistics Chapter 5 Flashcards

Key Concepts in Probability and Statistics

• Classical Method: Probability calculated as the ratio of the number of successful outcomes to the total number of outcomes in the sample space.
• Event: A specific set of outcomes derived from the sample space.
• Experiment: A defined activity where the result is uncertain.
• Law of Large Numbers: As experiments are repeated, the observed frequency of outcomes will stabilize around their expected probabilities.
• Law of Total Probability: The collective probabilities of all possible outcomes in a sample space equal one.
• Outcome: The result from a single trial of an experiment.
• Probability of Event A (P(A)): A numerical measure representing the likelihood of event A occurring.
• Probability Model: A structured representation showing possible outcomes and their probabilities, ensuring each probability falls between 0 and 1, and sums to 1.
• Tree Diagram: A visual representation used to depict all potential outcomes branching out from a starting point.
• Relative Frequency Method: Probability determined by dividing the occurrence of an event by the number of trials.
• Empirical Method: Another term for the relative frequency method; involves actual observed frequencies.
• Sample Space (S): The complete set of all possible outcomes for an experiment.
• Subjective Probability: Probability determined based on personal or subjective judgment rather than statistical analysis.
• Mutually Exclusive Events: Two events that cannot occur simultaneously; their intersection probability is zero (P(A and B) = 0).
• Disjoint: A synonym for mutually exclusive events.
• Complement of A: Represents all outcomes in the sample space that are not part of event A.
• Intersection of A and B: Outcomes that are shared by both events A and B; denoted as "AND".
• Union of A and B: Outcomes included in either event A or B; denoted as "OR".
• Addition Rule for A and B: Formula to find the probability of either event A or event B occurring, accounting for any overlap.
• Conditional Probability of B given A (P(B/A)): Probability of event B occurring after confirming that event A has happened.
• Independent Events: Two events where the occurrence of one does not affect the probability of the other.
• Multiplication Rule for Independent Events: The joint probability of independent events A and B equals the product of their individual probabilities (P(A) x P(B)).
• Multiplication Rule for Dependent Events: Takes into account the dependency of events; calculated as P(B/A) x P(A).
• 1% Rule: When the sample size is ≤ 1% of the population, events are treated as independent during successive selections.
• Sampling with Replacement: The same item can be chosen multiple times from the sample space.
• Sampling without Replacement: An item can only be selected once from the sample space.
• Combination: Choosing r selections from n options where order does not matter, and repetition is not allowed.
• Permutation: Arranging r selections from n options where order is significant and without repetition.
• Factorial (n!): The product of all positive integers up to n, representing the total arrangements possible.
• Multiplication Rule for Counting: Used to determine the total number of different outcomes when combining multiple events.

Test your understanding of key concepts from Statistics Chapter 5 with these flashcards. Definitions include classical method, event, experiment, and the law of large numbers. Perfect for students looking to reinforce their comprehension of statistical principles.