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Introductory Statistics Review

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Terms in this set (20)

  • What is the expected value (mean) in statistics?

    The expected value is the long-run average or mean of a random variable's possible values weighted by their probabilities.

  • Define standard deviation.

    Standard deviation measures the average amount of variability or dispersion around the mean in a data set.

  • What is a Venn diagram used for in probability?

    A Venn diagram visually represents sets and their relationships, such as intersections, unions, and complements in probability.

  • Explain the difference between conditional and unconditional probability.

    Conditional probability is the probability of an event given another event has occurred, while unconditional probability is the probability of an event without any conditions.

  • What is the formula for the probability of the union of two events A and B?

    P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

  • What is a sample space?

    The sample space is the set of all possible outcomes of a random experiment.

  • Define independent events.

    Two events are independent if the occurrence of one does not affect the probability of the other.

  • What is the binomial distribution used for?

    The binomial distribution models the number of successes in a fixed number of independent trials with the same probability of success.

  • What is the normal distribution?

    The normal distribution is a continuous probability distribution that is symmetric and bell-shaped, characterized by its mean and standard deviation.

  • How do you calculate a z-score?

    A z-score is calculated as \(z = \frac{X - \mu}{\sigma}\), measuring how many standard deviations a value X is from the mean μ.

  • What does the complement rule state?

    The complement rule states that P(Ac) = 1 - P(A), where Ac is the complement of event A.

  • Explain the difference between discrete and continuous random variables.

    Discrete random variables take countable values, while continuous random variables take any value in an interval.

  • What is the purpose of a probability distribution?

    A probability distribution describes how probabilities are assigned to each possible value of a random variable.

  • What is the law of large numbers?

    The law of large numbers states that as the number of trials increases, the sample mean approaches the expected value.

  • Define mutually exclusive events.

    Mutually exclusive events cannot occur at the same time; their intersection is empty.

  • What is a probability tree diagram used for?

    A probability tree diagram helps visualize and calculate probabilities of sequential events.

  • How do you calculate the mean of a binomial distribution?

    The mean of a binomial distribution is \(\mu = np\), where n is the number of trials and p is the probability of success.

  • What is the formula for variance?

    Variance is the average squared deviation from the mean, calculated as \(\sigma^2 = E[(X - \mu)^2]\).

  • What does 'unusual' mean in the context of probability?

    An unusual event is one with a low probability, often less than 5%.

  • What is the difference between population and sample?

    The population includes all members of a group, while a sample is a subset selected for study.