ISYE 6501 COMPREHENSIVE REVIEW
PAPER WITH SOLVED QUESTIONS
◉ Bernoulli Distribution
Answer: Single Trial with two possible outcomes
coin flip
◉ Bernoulli Distribution Formula
Answer: P success = (1-p failure)
◉ Binomial Distribution
Answer: Count of Successes in N Trials, what is the probability of
getting exactly x successes?
As binomial grows large, it converges to the normal distribution
◉ Binomial Distribution Formula
Answer: P(n=k)=C(n,k)*p^k*(1-p)^(n-k)
n=number of trials
k=target number
C=?
◉ Geometric Distribution
,Answer: How many trials needed before the first success/failure -
how many interviews before first job
◉ Poisson Distribution
Answer: Number of independent, identically distributed random
arrivals in a fixed time period
number of people arriving at an airport security gate
◉ Poisson Distribution Formula
Answer: P(x=k)=(l^k*e^(-l))/k!
l(lambda) = average number of arrivals per time period
k=number of successes
◉ Exponential Distribution
Answer: Time between consecutive arrivals (inter-arrival times)
Times between arriving at a airport security gate
◉ Memoryless property
Answer: When the probability of an arrival in the next t seconds is
the same regardless of how long it's been since the last arrival.
Discovered from data, not assumed
◉ Weibull Distribution
Answer: Time between successes/failures - how long an item lasts
,Extra parameter k controls shape of failure rate over time
◉ Distribution Fitting Cautions
Answer: Automatic fitting can find the best fit, but if it's the wrong
distribution, then it's probably just noise
◉ Q-Q Plot
Answer: Visually comparing 2 distributions, showing where they
differ and how - either 2 datasets or 1 dataset against theoretical
distribution
◉ Reading Q-Q Plot Deviations - Points on or near the 45°
diagonal
Answer: Distributions are a good match
◉ Reading Q-Q Plot Deviations - Points above diagonal at both
tails
Answer: Dataset 2 has more extreme values
◉ Reading Q-Q Plot Deviations - Points below diagonal at both
tails
Answer: Dataset 2 has less extreme values
◉ Reading Q-Q Plot Deviations - S-Curve shape (above left tail,
below right tail)
, Answer: Datset 2 is more right-skewed than dataset 1
◉ Reading Q-Q Plot Deviations - Points match in middle but
diverge at tails
Answer: Distributions match on average but differ in extreme
values
◉ Queuing Theory
Answer: Model systems where entities arrive, wait in a queue, and
are served. Analyzes wait times, queue lengths, and server
utilization
◉ Kendall Notation
Answer: Standard notation for describing queuing systems
arrival distribution/service distribution/number of
servers/population size, queue discipline
◉ Types of Simulation
Answer: Deterministic
Stochastic
Continuous-Time
Discrete-Event
◉ Deterministic Simulation
PAPER WITH SOLVED QUESTIONS
◉ Bernoulli Distribution
Answer: Single Trial with two possible outcomes
coin flip
◉ Bernoulli Distribution Formula
Answer: P success = (1-p failure)
◉ Binomial Distribution
Answer: Count of Successes in N Trials, what is the probability of
getting exactly x successes?
As binomial grows large, it converges to the normal distribution
◉ Binomial Distribution Formula
Answer: P(n=k)=C(n,k)*p^k*(1-p)^(n-k)
n=number of trials
k=target number
C=?
◉ Geometric Distribution
,Answer: How many trials needed before the first success/failure -
how many interviews before first job
◉ Poisson Distribution
Answer: Number of independent, identically distributed random
arrivals in a fixed time period
number of people arriving at an airport security gate
◉ Poisson Distribution Formula
Answer: P(x=k)=(l^k*e^(-l))/k!
l(lambda) = average number of arrivals per time period
k=number of successes
◉ Exponential Distribution
Answer: Time between consecutive arrivals (inter-arrival times)
Times between arriving at a airport security gate
◉ Memoryless property
Answer: When the probability of an arrival in the next t seconds is
the same regardless of how long it's been since the last arrival.
Discovered from data, not assumed
◉ Weibull Distribution
Answer: Time between successes/failures - how long an item lasts
,Extra parameter k controls shape of failure rate over time
◉ Distribution Fitting Cautions
Answer: Automatic fitting can find the best fit, but if it's the wrong
distribution, then it's probably just noise
◉ Q-Q Plot
Answer: Visually comparing 2 distributions, showing where they
differ and how - either 2 datasets or 1 dataset against theoretical
distribution
◉ Reading Q-Q Plot Deviations - Points on or near the 45°
diagonal
Answer: Distributions are a good match
◉ Reading Q-Q Plot Deviations - Points above diagonal at both
tails
Answer: Dataset 2 has more extreme values
◉ Reading Q-Q Plot Deviations - Points below diagonal at both
tails
Answer: Dataset 2 has less extreme values
◉ Reading Q-Q Plot Deviations - S-Curve shape (above left tail,
below right tail)
, Answer: Datset 2 is more right-skewed than dataset 1
◉ Reading Q-Q Plot Deviations - Points match in middle but
diverge at tails
Answer: Distributions match on average but differ in extreme
values
◉ Queuing Theory
Answer: Model systems where entities arrive, wait in a queue, and
are served. Analyzes wait times, queue lengths, and server
utilization
◉ Kendall Notation
Answer: Standard notation for describing queuing systems
arrival distribution/service distribution/number of
servers/population size, queue discipline
◉ Types of Simulation
Answer: Deterministic
Stochastic
Continuous-Time
Discrete-Event
◉ Deterministic Simulation
