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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 gives the probability that the random variable will equal a given
value
cumulative distribution function - ANSWER ✔✔-SOS
F:R --> [0,1]
Bernoulli distribution - ANSWER ✔✔-success or failure
X=1 success
X=0 failure
P(1) = P(X=1) = P
Created by ©EmilyCharlene 2025. All rights reserved.
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P(0) = P(X=0) = 1-P
Binomial distribution - ANSWER ✔✔-Let X represent the number of successes in n trials
X~Bin(n,p)
sequence of Bernoullis
Geometric distribution - ANSWER ✔✔-Let X equal the number of trials until a success occurs
Poisson random variable - ANSWER ✔✔-A random variable X, taking on values 0,1,2,3... is poisson w
parameter λ for some λ>0
counting process
counts events in a time period
exponential random variable - ANSWER ✔✔-time until some event occurs
memoryless property - ANSWER ✔✔-a non-negative random variable is memoryless if P{X>s+t | X>t} =
P{X>s}
we know X>t, so just need to prove greater than s
the lottery is memoryless
all exponential distributions are memoryless
discrete marginal probability distributions - ANSWER ✔✔-there are marginal distributions for each
random variable, formed by summing the joint PMF over the other variable.
continuous marginal probability distributions - ANSWER ✔✔-Rather than summing a discrete joint PMF,
we integrate a continuous joint PDF.
The marginal PDFs are used to make probability statements about one variable.
Created by ©EmilyCharlene 2025. All rights reserved.
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 gives the probability that the random variable will equal a given
value
cumulative distribution function - ANSWER ✔✔-SOS
F:R --> [0,1]
Bernoulli distribution - ANSWER ✔✔-success or failure
X=1 success
X=0 failure
P(1) = P(X=1) = P
Created by ©EmilyCharlene 2025. All rights reserved.
, 2|Page
P(0) = P(X=0) = 1-P
Binomial distribution - ANSWER ✔✔-Let X represent the number of successes in n trials
X~Bin(n,p)
sequence of Bernoullis
Geometric distribution - ANSWER ✔✔-Let X equal the number of trials until a success occurs
Poisson random variable - ANSWER ✔✔-A random variable X, taking on values 0,1,2,3... is poisson w
parameter λ for some λ>0
counting process
counts events in a time period
exponential random variable - ANSWER ✔✔-time until some event occurs
memoryless property - ANSWER ✔✔-a non-negative random variable is memoryless if P{X>s+t | X>t} =
P{X>s}
we know X>t, so just need to prove greater than s
the lottery is memoryless
all exponential distributions are memoryless
discrete marginal probability distributions - ANSWER ✔✔-there are marginal distributions for each
random variable, formed by summing the joint PMF over the other variable.
continuous marginal probability distributions - ANSWER ✔✔-Rather than summing a discrete joint PMF,
we integrate a continuous joint PDF.
The marginal PDFs are used to make probability statements about one variable.
Created by ©EmilyCharlene 2025. All rights reserved.
