Apply counting principles, permutations, and combinations to solve real-world problems.
Apply binomial and multinomial theorems to solve theoretical problems.
Describe a sample space and its events.
Apply the axioms of probability.
Compute the probability of an event.
Compute a conditional probability.
Apply the multiplication rule.
Use the law of total probability.
Employ Bayes' formula.
Determine if two given events are independent.
Compute the probability mass function of a discrete random variable.
Compute the expectation of a discrete random variable.
Compute the variance of a discrete random variable.
Master Bernoulli and binomial random variables.
Master Poisson random variables.
Master geometric and negative binomial random variables.
Master hypergeometric random variables.
Determine if a function is a probability density function.
Compute event probabilities and distribution functions using density functions.
Compute the expectation and variance of a continuous random variable.
Master uniform random variables.
Master normal random variables.
Master exponential random variables.
Find the joint distribution function of two random variables.
Compute joint probabilities.
Determine if given random variables are independent.
Determine the distributions of sums of independent random variables.
Calculate conditional distribution functions.
Find the expectation of a sum of random variables.
Compute covariance, variance of sums, and correlations.
Compute conditional expectations.
Find moment generating functions.
Apply the Markov and Chebyshev inequalities.
Master the central limit theorem.
Master laws of large numbers.