ISyE 2027 review basics Questions + Answers Graded A+

ISyE 2027 review basics
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

P(AB) = P(A|B) x P(B)
= P(B|A) x P(A) - ✔️✔️Multiplication Rule

2^k

month a baby is born has 2^12 possible events - ✔️✔️How many subsets does a set
with k elements have?

i) P(A|B) = P(A)
ii) P(B|A)=P(B)
iii) P(AB) = P(A) * P(B) - ✔️✔️A and B are independent if

P(A) = P(A|B)*P(B) + P(A|Bc)*P(Bc)
P(A) = summation of P(A|Ci)*P(Ci) from k=1 to m - ✔️✔️Law of Total Probability

P(A|B) = P(B|A) x P(A)
/ P(B) - ✔️✔️Bayes Theorem

P(A|B) = P(AB) / P(B) - ✔️✔️Conditional Probability

i) P(sample space) = 1
ii) 0<=P(A)<=1
iii) if A and B are disjoint, P(A union B) = P(A)+P(B) - ✔️✔️Probability Axioms


1-P(A) - ✔️✔️P(Ac)=

P(A)+P(B) - P(AB) - ✔️✔️P(A union B)=