Discrete probability fundamentals as covered in a discrete mathematics course, distinct from a full statistics course.
29 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a sample space in probability?
- The set of all possible outcomes of a random experiment.
- What is an event in probability?
- A subset of the sample space, a collection of one or more outcomes.
- Define the probability of an event A.
- The ratio of favorable outcomes to total possible outcomes, denoted P(A).
- What is P(complement of A) in terms of P(A)?
- P(A^c) = 1 - P(A)
- State the addition rule for the union of two events A and B.
- P(A union B) = P(A) + P(B) - P(A intersect B)
- What is the probability of the union of two mutually exclusive events?
- P(A union B) = P(A) + P(B) (no intersection term, since P(A intersect B) = 0)
- Define conditional probability P(A|B).
- The probability of event A occurring given that event B has occurred, equal to P(A intersect B) / P(B).
- When are two events A and B independent?
- When P(A intersect B) = P(A) * P(B), or equivalently, when P(A|B) = P(A).
- State the multiplication rule for any two events A and B.
- P(A intersect B) = P(A) * P(B|A) = P(B) * P(A|B)
- State Bayes' theorem.
- P(A|B) = P(B|A) * P(A) / P(B)
- What is the expected value of a discrete random variable X?
- E[X] = sum of (x * P(X = x)) for all values x
- Define the variance of a random variable X.
- Var(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2
- What is a permutation of n objects taken r at a time?
- An ordered arrangement of r objects from n objects, denoted P(n,r) or nPr, equal to n! / (n-r)!
- What is a combination of n objects taken r at a time?
- An unordered selection of r objects from n objects, denoted C(n,r) or nCr, equal to n! / (r! * (n-r)!)
- State the binomial probability formula.
- P(X = k) = C(n,k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success on each trial.