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Introductory Statistics: Probability and Binomial Distributions

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Terms in this set (20)

  • Law of Large Numbers
    As the number of trials increases, the experimental probability values approach the classical probability.
  • Characteristics of Probability Distributions
    Probabilities are between 0 and 1 inclusive, and the sum of all probabilities equals 1.
  • Binomial Distribution Outcomes
    Binomial distributions have exactly two outcomes: success or failure.
  • Complement Rule in Probability
    The probability of the complement of an event is \(1 - P(\text{event})\).
  • Addition Rule for Probability of A or B
    P(A or B) = P(A) + P(B) - P(A and B) to avoid double counting the overlap.
  • Multiplication Rule for Independent Events
    P(A and B) = P(A) × P(B) if events A and B are independent.
  • Conditional Probability Formula
    P(B | A) = P(A and B) / P(A), where the denominator is the probability of event A.
  • Mean of a Binomial Distribution
    The mean is calculated as \(\mu = n p\), where n is trials and p is success probability.
  • Variance of a Binomial Distribution
    The variance is \(\sigma^2 = n p q\), where q = 1 - p.
  • Standard Deviation of a Binomial Distribution
    The standard deviation is \(\sigma = \sqrt{n p q}\).
  • Using Binomial Distribution Tables
    Write the inequality for the desired probability and use the table to find the corresponding values.
  • Probability Values Range
    All probability values satisfy \(0 \leq P \leq 1\).
  • Sum of Probabilities in a Distribution
    The sum of all probabilities in a probability distribution equals 1.
  • Interpreting P(A and B)
    P(A and B) represents the probability that both events A and B occur simultaneously.
  • Interpreting P(A or B)
    P(A or B) represents the probability that at least one of the events A or B occurs.
  • Success and Failure in Binomial Trials
    Each trial results in either a success or a failure, with fixed probabilities.
  • Calculating Complement Probability
    To find the probability that an event does not occur, subtract its probability from 1.
  • Reading Probability Tables
    Use the given tables to find probabilities for events or cumulative probabilities based on inequalities.
  • Probability of Independent Events
    If events are independent, the probability of both occurring is the product of their individual probabilities.
  • Notation for Probability of Conditional Events
    P(B | A) denotes the probability of event B occurring given that event A has occurred.