CMPE107 Notes

• Axioms: A proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. • Bernoulli Distribution: A discrete binary distribution determined by the probability of success or failure. • Bernoulli Random Variable: Typically a binomial random variable expressed as the function of two parameters: the number of trials and the probability of success. • Bernoulli Trials: An experiment of some number of trials with the probability of success in a given trial. • Birth/Death Process: A case of the time-continuous Markov process where states indicate the number of elements in a system. Useful for modeling populations in mechanical, electrical and natural systems (eg. human population, service queues). • Certain: An occurrence of an event that is inevitable. • Conditional Probability: The probability that event A occurs when the sample space is limited to event B. This is read “the probability of A, given B”. • Conditioning Event: An event that constrains another event to a subset of itself. • Correlation: A statistical relationship between two dependent random variables. • Covariance: How much two random variables change together. • Counterexample: An example that contradicts a proposition and invalidates the result. • Cumulative Distribution Function: A probability function that is the sum of all probabilities up to some given value of the function (F (t) = P (X ≤ t)). • Expected Value: The weighted average or mean value of all random variable values. • Events: A subset of the sample space. • Impossible: An occurrence of an event that will never happen. • Independence: The occurrence of an event having no effect on the probability of another.