ISYE 2027
ISYE 2027
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Examen
ISYE 2027 - exam 1 Questions and Answers Fully Solved Latest Update 2025-2026
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---5julio 20252024/2025A+
- ISYE 2027 - exam 1 Questions and Answers Fully Solved Latest Update 
 
combinatorics - Answers branch of discrete mathematics that studies the arrangement of objects 
enumeration - Answers part of combinatorics that explores the ways we can count objects with certain properties 
product rule - Answers to find the number of ways of doing something, multiply the number of choices available at each stage 
sum rule - Answers if a task can be done either in one of n1 ways or in one of n2 ways, where...
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TutorJosh
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Examen
ISyE 2027 Final Exam Practice Questions and Answers 100% Pass
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---6diciembre 20242024/2025A+
- ISyE 2027 Final Exam Practice 
Questions and Answers 100% Pass 
Discrete uniform distribution - ANSWER -sos 
probability is... - ANSWER -starting with an animal and figuring out what footprints it will make 
statistics is... - ANSWER -seeing a footprint and guessing the animal 
disjoint - ANSWER -A ∩ B = ∅ therefore P(A|B) = 0 
independence - ANSWER -P(A|B) = P(A) 
P(A|B) - ANSWER -P(A∩B)/P(B) 
probability mass function (pmf) - ANSWER -p(a) = P(X=a) 
-The pmf of a discrete random variable ...
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EmilyCharlene
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Examen
ISYE 2027 Exam Questions and Answers Solved Correctly
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---2julio 20252024/2025A+
- ISYE 2027 Exam Questions and Answers Solved Correctly 
Bernoulli - Answers An event either occurs or does not occur 
Bernoulli Parameter - Answers P 
Bernoulli PMF - Answers P if 1, 1-P if 0, 0 otherwise 
Bernoulli's E[x] - Answers P 
Bernoulli Variance - Answers p(1-p) 
Binomial - Answers Number of successes within n trials 
Binomial Parameters - Answers (n,p) 
Binomial PMF - Answers (nCk)(p^k)(1-p)^(n-k) 
Binomial E[x] - Answers np 
Binomial Variance - Answers np(1-p) 
Geometric - Answers ...
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TutorJosh
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Examen
ISYE 2027 Midterm 1 Exam Questions and Answers 100% Pass
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---4diciembre 20242024/2025A+
- ISYE 2027 Midterm 1 Exam Questions 
and Answers 100% Pass 
Experiment - ANSWER -any situation involving some element of uncertainty/randomness, where 
different possible outcomes can be identified in advance 
Outcome - ANSWER -each possible thing that can happen as the result of an experiment 
Sample Space - ANSWER -all possible outcomes put together 
Events - ANSWER -subsets of the sample space 
Probability - ANSWER -numbers we assign to each event, such that is measures the "size" of the...
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EmilyCharlene
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Examen
ISyE 2027 Final Exam latest questions and answers all are correct graded A+
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--4diciembre 20242024/2025A+Disponible en un paquete
- 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 failure 
P(1) = P(X=1) = P 
P(0) = P(X=0) = 1-P 
Binomial distribution - ️️Let X represent the number of successes in n trials 
X~Bin(n,p) 
sequence of Bernoullis 
Geometric distribution - ️️L...
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Brainarium
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Examen
ISyE 2027 review basics Questions + Answers Graded A+
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--3diciembre 20242024/2025A+Disponible en un paquete
- 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) 
i...
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Brainarium
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Examen
ISYE 2027 Midterm 1 Questions and Answers(A+ Solution guide)
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--3diciembre 20242024/2025A+Disponible en un paquete
- 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 either A or B (or both). A ∪ B only 
occurs if at least one of the events A and B occurs 
A: event {Born in the first half of the year} 
B: event {Born in a long month} 
A ∪ B? - ️️A ∪ B = {Ja...
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Brainarium
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Examen
ISyE 2027 review basics Exam Questions and Answers 100% Pass
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---4diciembre 20242024/2025A+
- ISyE 2027 review basics Exam 
Questions and Answers 100% Pass 
i) P(A|B) = P(A) 
ii) P(B|A)=P(B) 
iii) P(AB) = P(A) * P(B) - ANSWER -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 - ANSWER -Law of Total Probability 
P(A|B) = P(B|A) x P(A) 
/ P(B) - ANSWER -Bayes Theorem 
P(A|B) = P(AB) / P(B) - ANSWER -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) - ANS...
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EmilyCharlene
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Examen
ISyE 2027 EXAM 1 QUESTIONS AND ANSWERS 100% PASS
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---2diciembre 20242024/2025A+
- ISyE 2027 EXAM 1 QUESTIONS AND 
ANSWERS 100% PASS 
sample space - ANSWER -Ω - set of possible outcomes 
event - ANSWER -F - subset of Ω. An event is said to occur or be true when the experiment is 
performed if the outcome is in the event 
∩ - ANSWER -AND - INTERSECTION 
(this can also be written as A∩B = AB) 
∪ - ANSWER -OR - UNION 
B^c - ANSWER -COMPLEMENT OF B
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EmilyCharlene