BackIntroductory Statistics Key Concepts
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Terms in this set (22)
The expected value is the long-run average or mean value of a random variable over many trials.
Standard deviation measures the average amount of variation or dispersion of a set of values.
The complement rule states that the probability of an event not occurring is 1 minus the probability that it does occur.
Conditional probability is the probability of an event occurring given that another event has already occurred.
The sample space is the set of all possible outcomes of a probability experiment.
Independent events are events where the occurrence of one does not affect the probability of the other.
The binomial distribution models the number of successes in a fixed number of independent trials with the same probability of success.
The normal distribution is a symmetric, bell-shaped distribution characterized by its mean and standard deviation.
A z-score measures how many standard deviations a data point is from the mean.
The probability of either event A or event B occurring is the sum of their probabilities minus the probability of both occurring.
The probability of both event A and event B occurring is the product of the probability of A and the conditional probability of B given A.
An unusual event is one with a probability less than 0.05, indicating it is unlikely to occur.
Venn diagrams visually represent relationships between sets, including intersections, unions, and complements.
The expected value is calculated as \(E(X) = \sum x_i p(x_i)\), summing all outcomes times their probabilities.
Standard deviation is \(\sigma = \sqrt{\sum (x_i - \mu)^2 p(x_i)}\) for a probability distribution.
Conditional probability is \(P(A|B) = \frac{P(A \cap B)}{P(B)}\), the probability of A given B.
Probability of A or B is \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\).
Probability of A and B is \(P(A \cap B) = P(A) \times P(B|A)\).
The normal distribution is symmetric, with mean = median = mode, and total area under curve equals 1.
Dice rolls illustrate sample space and probability calculations for equally likely outcomes.
A sample is a subset of a population used to estimate characteristics of the whole population.
Probability quantifies uncertainty and underpins statistical inference and decision making.