ISYE 6644 MIDTERM AND FINAL Updated Exam 2026 WITH Recent
Newest Verified And Well Analyzed Exam Questions (Actual Exam
2026-2027) Correct Detailed & Verified ANSWERS (100% Accurate
Solutions) ALREADY GRADED A+||NEWEST VERSION Of The Exam
Guarantee Pass!!
TRUE or FALSE? If you can't find a good theoretical distribution to model a certain
random variable, you might want to use the empirical distribution of the data to
do so. -ANSWER-True
TRUE or FALSE? The convolution method involves sums of random variables. -
ANSWER-True
Suppose that U1 and U2 are PRNs. Whats the distribution of U1 + U2? -ANSWER-
Triangular(0,1,2)
YES or NO? As in the notes, suppose that I want to generate a simple Unif(2/3,1)
via A-R. Suppose I generate a PRN U1 = 0.16. Do I accept U1 as my Unif(2/3,1)? -
ANSWER-No. In this example, we only accept U1 >= 2/3; so we reject and try
again until we meet that condition.
TRUE or FALSE? The proof that A-R works is really easy. -ANSWER-False
Suppose that X is a continuous RV with p.d.f. f(x) = 30x^4(1-x) for 0<x<1. Why is
acceptance-rejection a good method to use to generate X? -ANSWER-Because the
c.d.f. of X is very hard to invert.
,Unif(0,1) PRNs can be used to generate which of the following random entities? -
ANSWER-Exp(lambda) random variates, Nor(0,1) random variates, Triangular
random variates, Bern(p) random variates, Nonhomogeneous Poisson processes,
and just about anything else.
If X is an Exp(lambda) random variable with c.d.f. F(x) = 1-e^(-lambdax), what's
the distribution of the random variable 1-e^(-lambdaX)? -ANSWER-Unif(0,1).
Inverse transform theroem.
If U is a Unif(0,1) random variable, what's the distribution of -1/lambda(ln(U))? -
ANSWER-Exp(lambda)
If X is a Nor(0,1) random variate, and Φ ( x ) is the Nor(0,1) c.d.f., what is the
distribution of Φ ( X )? -ANSWER-Uniform. By the inverse transform theorem, Φ (
X ) ~ Unif(0,1).
How would you simulate the sum of two 6-sided dice tosses? -ANSWER-[6U1] +
[6U2]
If U is Unif(0,1), how can we simulate a Geom(0.6) random variate? -ANSWER-
[ln(U)/ln(0.4)] or [ln(1-U)/ln(0.4)]
Suppose that U and V are PRNs. Let X=U+V. Simulate this 5000 times, and draw a
histogram of the 5000 numbers. What p.d.f. does the histogram look like? -
ANSWER-Triangular.
In general, the majorizing function t(x) is itself a p.d.f. f(x)? -ANSWER-False
, Suppose that X is a continuous RV with p.d.f. f(x) = 30x^4(1-x) for 0<x<1. What's a
good method that you can use to generate a realization of X? -ANSWER-
Acceptance-Rejection
Consider four observations from some unknown distribution, X1=1.5, X2 = -3.7,
X3=2.7, and X4= 0.6. What is the fourth order statistic, denoted X(4)? -ANSWER-
2.7. X(4) means the largest of the sample of 4 observations.
Which of the following are true? -ANSWER-The closer the majorizing function t(x)
is to the true p.d.f. f(x), the more efficient the A-R algorithm is; h(y) = t(y)/integral
of t(x) is itself a p.d.f., random variates from h(y) should be "easy" to generate
Suppose that an airline can experience three types of departure delays - A, B, and
C, which occur with probabilities 0.4, 0.1, and 0.5, respectively. Delays A, B, and C
are exponential, normal, and Weibull, respectively. YES or NO? Would the
composition method be a good choice to generate a delay time for this scenario?
-ANSWER-Yes. Composition would be much more efficient than figuring out and
delaying with the crazy c.d.f. of the overall delay.
Let H and W denote a person's height and weight. Which of the following best
describes the joint distribution of (H,W)? -ANSWER-Bivariate normal distribution
with positive correlation coefficient.
The multivariate normal distribution's covariance matrix sigma can be
decomposed into the form sigma = CC^T. What does the C informally stand for? -
ANSWER-Cholesky
TRUE or FALSE? The time between Poisson(lambda) arrivals are i.i.d. Exp(lambda).
-ANSWER-True. As long as lambda doesn't change over time.
Newest Verified And Well Analyzed Exam Questions (Actual Exam
2026-2027) Correct Detailed & Verified ANSWERS (100% Accurate
Solutions) ALREADY GRADED A+||NEWEST VERSION Of The Exam
Guarantee Pass!!
TRUE or FALSE? If you can't find a good theoretical distribution to model a certain
random variable, you might want to use the empirical distribution of the data to
do so. -ANSWER-True
TRUE or FALSE? The convolution method involves sums of random variables. -
ANSWER-True
Suppose that U1 and U2 are PRNs. Whats the distribution of U1 + U2? -ANSWER-
Triangular(0,1,2)
YES or NO? As in the notes, suppose that I want to generate a simple Unif(2/3,1)
via A-R. Suppose I generate a PRN U1 = 0.16. Do I accept U1 as my Unif(2/3,1)? -
ANSWER-No. In this example, we only accept U1 >= 2/3; so we reject and try
again until we meet that condition.
TRUE or FALSE? The proof that A-R works is really easy. -ANSWER-False
Suppose that X is a continuous RV with p.d.f. f(x) = 30x^4(1-x) for 0<x<1. Why is
acceptance-rejection a good method to use to generate X? -ANSWER-Because the
c.d.f. of X is very hard to invert.
,Unif(0,1) PRNs can be used to generate which of the following random entities? -
ANSWER-Exp(lambda) random variates, Nor(0,1) random variates, Triangular
random variates, Bern(p) random variates, Nonhomogeneous Poisson processes,
and just about anything else.
If X is an Exp(lambda) random variable with c.d.f. F(x) = 1-e^(-lambdax), what's
the distribution of the random variable 1-e^(-lambdaX)? -ANSWER-Unif(0,1).
Inverse transform theroem.
If U is a Unif(0,1) random variable, what's the distribution of -1/lambda(ln(U))? -
ANSWER-Exp(lambda)
If X is a Nor(0,1) random variate, and Φ ( x ) is the Nor(0,1) c.d.f., what is the
distribution of Φ ( X )? -ANSWER-Uniform. By the inverse transform theorem, Φ (
X ) ~ Unif(0,1).
How would you simulate the sum of two 6-sided dice tosses? -ANSWER-[6U1] +
[6U2]
If U is Unif(0,1), how can we simulate a Geom(0.6) random variate? -ANSWER-
[ln(U)/ln(0.4)] or [ln(1-U)/ln(0.4)]
Suppose that U and V are PRNs. Let X=U+V. Simulate this 5000 times, and draw a
histogram of the 5000 numbers. What p.d.f. does the histogram look like? -
ANSWER-Triangular.
In general, the majorizing function t(x) is itself a p.d.f. f(x)? -ANSWER-False
, Suppose that X is a continuous RV with p.d.f. f(x) = 30x^4(1-x) for 0<x<1. What's a
good method that you can use to generate a realization of X? -ANSWER-
Acceptance-Rejection
Consider four observations from some unknown distribution, X1=1.5, X2 = -3.7,
X3=2.7, and X4= 0.6. What is the fourth order statistic, denoted X(4)? -ANSWER-
2.7. X(4) means the largest of the sample of 4 observations.
Which of the following are true? -ANSWER-The closer the majorizing function t(x)
is to the true p.d.f. f(x), the more efficient the A-R algorithm is; h(y) = t(y)/integral
of t(x) is itself a p.d.f., random variates from h(y) should be "easy" to generate
Suppose that an airline can experience three types of departure delays - A, B, and
C, which occur with probabilities 0.4, 0.1, and 0.5, respectively. Delays A, B, and C
are exponential, normal, and Weibull, respectively. YES or NO? Would the
composition method be a good choice to generate a delay time for this scenario?
-ANSWER-Yes. Composition would be much more efficient than figuring out and
delaying with the crazy c.d.f. of the overall delay.
Let H and W denote a person's height and weight. Which of the following best
describes the joint distribution of (H,W)? -ANSWER-Bivariate normal distribution
with positive correlation coefficient.
The multivariate normal distribution's covariance matrix sigma can be
decomposed into the form sigma = CC^T. What does the C informally stand for? -
ANSWER-Cholesky
TRUE or FALSE? The time between Poisson(lambda) arrivals are i.i.d. Exp(lambda).
-ANSWER-True. As long as lambda doesn't change over time.
