ISyE 2027 EXAM PACKAGE DEAL SCORED A+

mutually exclusive - ️️two or more events are said to be mutually exclusive when at most one of the events can be true EiEj = ∅ whenever i =/ j which means that the events are disjoint sets partition - ️️collection of subsets. If A is an event, then A and A^c form a partition of Ω ...

summation of ar^k from k = 0 to infinity converges to a/(1-r) - ️️Geometric Series summation of x^k/k! from k=0 to infinity = e^x - ️️Exponential Series n! - ️️Ordering n objects n! / (n-k)! - ️️Ordering k out of n objects (n c k) = n!/(n-k)!k! - ️️Choosing k out of n objects...

Intersection A ∩ B - ️️the set of outcomes that belong to both A and B occurs if and only if both A and B occur A: event {Born in the first half of the year} B: event {Born in a long month} A ∩ B? - ️️A ∩ B = {Jan, Mar, May} Union A ∪ B - ️️set of outcomes that belongs to ei...

probability mass function (pmf) - ️️p(a) = P(X=a) -The pmf of a discrete random variable gives the probability that the random variable will equal a given value cumulative distribution function - ️️SOS F:R --> [0,1] Bernoulli distribution - ️️success or failure X=1 success X=0 ...