Vocabulary Builder
1. Sample Space: The set of all possible outcomes of a random experiment.
2. Event: A subset of the sample space, representing a specific outcome or a collection of outcomes.
3. Probability: A measure of the likelihood of an event occurring, typically represented as a number between 0 and 1.
4. Probability Function: A function that assigns probabilities to events in the sample space, satisfying certain properties (such as non-negativity and additivity).
5. Random Variable: A variable that takes on values determined by the outcome of a random experiment.
6. Probability Distribution: The set of all possible values of a random variable and their corresponding probabilities.
7. Joint Probability: The probability of the simultaneous occurrence of two or more events.
8. Conditional Probability: The probability of an event given that another event has occurred.
9. Independence: Two events are independent if the occurrence or non-occurrence of one does not affect the probability of the other.
10. Complementary Event: The event consisting of all outcomes that are not in a given event.
11. Union of Events: The event that consists of outcomes that belong to either or both of two events.
12. Intersection of Events: The event that consists of outcomes that belong to both of two events.
13. Mutually Exclusive Events: Two events are mutually exclusive if they cannot occur simultaneously.
14. Counting Techniques: Methods used to count the number of outcomes in a sample space, such as permutations and combinations.
15. Expected Value: The average value of a random variable, weighted by their probabilities.
16. Variance: A measure of the spread or dispersion of a random variable around its expected value.
17. Bernoulli Trial: A random experiment with two possible outcomes, usually referred to as success and failure.
18. Binomial Distribution: A probability distribution that models the number of successes in a fixed number of independent Bernoulli trials.
19. Geometric Distribution: A probability distribution that models the number of trials needed to achieve the first success in a sequence of independent Bernoulli trials.
20. Poisson Distribution: A probability distribution that models the number of events occurring in a fixed interval of time or space, under certain assumptions.