ISYE 6644 OAN 1 SIMULATION
CERTIFICATION SCRIPT 2026 QUESTIONS
WITH SOLUTIONS GRADED A+
◍ Who is Dr. Harold Shipman?.
Answer: He killed his patients using heroin overdosesCaught after carelessly
revising a patient's will, leaving all her assets to himselfDoctored his records
to show his patients had needed morphine but the software recorded the
dates of these modificationshung himself in prison
◍ What are confidence intervals and what do they mean?(M2L16).
Answer: Gives bounds around your point estimate (like x-bar) that give a
certain confidence level (e.g., 95%) that the true population mean falls
within the CI around the estimate.*Crucial for hypothesis testing.Example:If
you estimate the average height of students as 170 cm with a 95%
confidence interval of [168 cm, 172 cm], it means that:Important
interpretation: If you repeated the sampling process many times, about 95%
of the intervals you compute would contain the true population mean.It does
not mean there is a 95% probability that the true mean is inside this specific
interval.
◍ What is the derivative of ln(x).
Answer: 1 / x
◍ Suppose that we are using some estimator to estimate an unknown
parameter . Further suppose that has a bias of 3 and a variance of 5.
What is 's mean squared error?.
Answer: MSE = 2 + Variance = 14.
◍ What is the central limits theorem?.
Answer: In probability theory, the central limit theorem establishes that, in
, some situations, when independent random variables are added, their
properly normalized sum tends toward a normal distribution even if the
original variables themselves are not normally distributed.
◍ What is a conditional wait?.
Answer: A conditional wait is a duration of time of unspecified length.ex:
customer waiting time.
◍ What is the derivative of cos(x).
Answer: -sin(x)
◍ In statistics, what does it mean for a point estimator to be
"unbiased?"(M2L14).
Answer: The expected value of your point estimator (e.g., x-bar) should
equal the parameter it is trying to estimate (e.g., mu).*A good point
estimator also has low variance (see MSE)
◍ What theorem allows you to find the expected value of any function of a
random variable, h(X), without needing a know the distribution of h(X)?
You only need to know the original distribution of the RV, X (M2, L7)..
Answer: LOTUS, Law of the Unconscious Statistician.
◍ What is the invariance property of the MLE for a parameter theta, and why
is it useful?(M2L15).
Answer: This property says that if you find the MLE of some parameter,
theta, then this estimate can be used in a function to get the MLE for the
function, too!Example: if you find the MLE of the mean, you can use this
value to calculate the MLE for variance with a simple formula (instead of
actually calculating variance with the MLE process).
◍ Which of the following is NOT a discrete distribution (M2L12)?a)
Bernoullib) Geometricc) Triangulard) Poissone) Binomial.
Answer: c) Triangular is continuous
◍ What are the three properties that define a typical Poisson counting
process?(M2L12).
Answer: 1. Arrivals only occur one at a time at avg rate (lambda)2. Time
, increments are independent of each other.3. Increments are stationary (e.g.,
length of time is the only thing that affects # of arrivals. Arrivals 3-4pm
have same probability as arrivals from 1-2am). homogeneous process.
◍ What is the process-interaction approach?.
Answer: 1. Create customers every once in a while.2. Process (serve) them,
maybe after waiting in line.3. Dispose of the customers after they're done
being processed.
◍ What is the method of batch means in analyzing steady-state simulations?.
Answer: -Make one long run (vs. many shorter reps)-warm up simulation
before collecting data-chop remaining observations into contiguous
batches-sample means from each batch are approximately i.i.d. normal-use
classical statistics on the i.i.d. batch means
◍ What important concept in probability theory states that regardless of the
original probability distribution (e.g., exponential), if you get the
distribution of your iid sample means, the distribution of sample means
converges to normal. This is NOT the same as saying that the sample mean
converges to the true population mean..
Answer: Central Limit Theorem (CLT). Deals with the shape (distribution)
of the sample means.Cauchy distribution is the EXCEPTION to CLT!
◍ For two variables, X and Y, that are jointly distributed: if you want to find
the marginal pdf of X (f_subX_(X)), you integrate across all values of....
Answer: y.Take dy (this means that your bounds of integration will most
likely not include y, e..g, will be in terms of x). -x <= y <= x
◍ True or False: a pdf corresponds to a discrete probability distribution..
Answer: False: a pdf corresponds to a continuous distribution and a pmf
corresponds to discrete.
◍ Of the common point estimators in statistics, which one is biased?(M2L14).
Answer: S = the sample st. dev. is biased for sigma, the true st. dev.*The
sample mean (X-bar) and sample variance (S^2) are unbiased estimators,
though!
CERTIFICATION SCRIPT 2026 QUESTIONS
WITH SOLUTIONS GRADED A+
◍ Who is Dr. Harold Shipman?.
Answer: He killed his patients using heroin overdosesCaught after carelessly
revising a patient's will, leaving all her assets to himselfDoctored his records
to show his patients had needed morphine but the software recorded the
dates of these modificationshung himself in prison
◍ What are confidence intervals and what do they mean?(M2L16).
Answer: Gives bounds around your point estimate (like x-bar) that give a
certain confidence level (e.g., 95%) that the true population mean falls
within the CI around the estimate.*Crucial for hypothesis testing.Example:If
you estimate the average height of students as 170 cm with a 95%
confidence interval of [168 cm, 172 cm], it means that:Important
interpretation: If you repeated the sampling process many times, about 95%
of the intervals you compute would contain the true population mean.It does
not mean there is a 95% probability that the true mean is inside this specific
interval.
◍ What is the derivative of ln(x).
Answer: 1 / x
◍ Suppose that we are using some estimator to estimate an unknown
parameter . Further suppose that has a bias of 3 and a variance of 5.
What is 's mean squared error?.
Answer: MSE = 2 + Variance = 14.
◍ What is the central limits theorem?.
Answer: In probability theory, the central limit theorem establishes that, in
, some situations, when independent random variables are added, their
properly normalized sum tends toward a normal distribution even if the
original variables themselves are not normally distributed.
◍ What is a conditional wait?.
Answer: A conditional wait is a duration of time of unspecified length.ex:
customer waiting time.
◍ What is the derivative of cos(x).
Answer: -sin(x)
◍ In statistics, what does it mean for a point estimator to be
"unbiased?"(M2L14).
Answer: The expected value of your point estimator (e.g., x-bar) should
equal the parameter it is trying to estimate (e.g., mu).*A good point
estimator also has low variance (see MSE)
◍ What theorem allows you to find the expected value of any function of a
random variable, h(X), without needing a know the distribution of h(X)?
You only need to know the original distribution of the RV, X (M2, L7)..
Answer: LOTUS, Law of the Unconscious Statistician.
◍ What is the invariance property of the MLE for a parameter theta, and why
is it useful?(M2L15).
Answer: This property says that if you find the MLE of some parameter,
theta, then this estimate can be used in a function to get the MLE for the
function, too!Example: if you find the MLE of the mean, you can use this
value to calculate the MLE for variance with a simple formula (instead of
actually calculating variance with the MLE process).
◍ Which of the following is NOT a discrete distribution (M2L12)?a)
Bernoullib) Geometricc) Triangulard) Poissone) Binomial.
Answer: c) Triangular is continuous
◍ What are the three properties that define a typical Poisson counting
process?(M2L12).
Answer: 1. Arrivals only occur one at a time at avg rate (lambda)2. Time
, increments are independent of each other.3. Increments are stationary (e.g.,
length of time is the only thing that affects # of arrivals. Arrivals 3-4pm
have same probability as arrivals from 1-2am). homogeneous process.
◍ What is the process-interaction approach?.
Answer: 1. Create customers every once in a while.2. Process (serve) them,
maybe after waiting in line.3. Dispose of the customers after they're done
being processed.
◍ What is the method of batch means in analyzing steady-state simulations?.
Answer: -Make one long run (vs. many shorter reps)-warm up simulation
before collecting data-chop remaining observations into contiguous
batches-sample means from each batch are approximately i.i.d. normal-use
classical statistics on the i.i.d. batch means
◍ What important concept in probability theory states that regardless of the
original probability distribution (e.g., exponential), if you get the
distribution of your iid sample means, the distribution of sample means
converges to normal. This is NOT the same as saying that the sample mean
converges to the true population mean..
Answer: Central Limit Theorem (CLT). Deals with the shape (distribution)
of the sample means.Cauchy distribution is the EXCEPTION to CLT!
◍ For two variables, X and Y, that are jointly distributed: if you want to find
the marginal pdf of X (f_subX_(X)), you integrate across all values of....
Answer: y.Take dy (this means that your bounds of integration will most
likely not include y, e..g, will be in terms of x). -x <= y <= x
◍ True or False: a pdf corresponds to a discrete probability distribution..
Answer: False: a pdf corresponds to a continuous distribution and a pmf
corresponds to discrete.
◍ Of the common point estimators in statistics, which one is biased?(M2L14).
Answer: S = the sample st. dev. is biased for sigma, the true st. dev.*The
sample mean (X-bar) and sample variance (S^2) are unbiased estimators,
though!
