ISYE 6644 Week 9 Homework Simulation
Attempt History
Score for this quiz: 12 out of 16
Question 1
pts
(Lesson 7.1: Introduction to Random Variate Generation.) Unif(0,1) PRNs can be used to generate
which of the following random entities?
a. Exp( ) random variates
b. Nor(0,1) random variates
c. Triangular random variates
d. Bern( ) random variates
e. Nonhomogeneous Poisson processes
f. All of the above --- and just about anything else!
(f).
Question 2
pts
(Lesson 7.2: Inverse Transform Theorem --- Intro.) If is an Exp( ) random variable with c.d.f.
, what's the distribution of the random variable ?
a. Unif(0,1)
b. Nor(0,1)
c. Triangular
d. Exp( )
e. None of the above
Note that , where the last step follows by the Inverse Transform
Theorem. Thus, the correct answer is (a).
Question 3
pts
(Lesson 7.2: Inverse Transform Theorem --- Intro.) If is a Unif(0,1) random variable, what's the
distribution of ?
a. Unif(0,1)
b. Nor(0,1)
, c. Triangular
d. Exp( )
e. None of the above
Since and are both Unif(0,1) (by symmetry), we have
where the last step follows from Lesson 2's Inverse Transform
Theorem example. Thus, the answer is (d).
Question 4
pts
(Lesson 7.2: Inverse Transform Theorem --- Intro.) Suppose that are i.i.d.
Unif(0,1) random variables. Using Excel (or your favorite programming language), simulate
. Draw a histogram of the 5000 numbers. What p.d.f.
does the histogram look like?
a. Uniform
b. Normal
c. Triangular
d. Exponential
e. Bernoulli
By the Inverse Transform Theorem, all of the 's are Exp( ). Since we have a histogram of 5000
of these, it really ought to look like an exponential p.d.f., , . Thus, the answer is (d).
Question 5
pts
(Lesson 7.3: Inverse Transform --- Continuous Examples.) Suppose the c.d.f. of is
, and demonstrate with .
. Then , and so . Plugging in
, we
. Thus, the correct answer is (c)
Question 6
pts
Attempt History
Score for this quiz: 12 out of 16
Question 1
pts
(Lesson 7.1: Introduction to Random Variate Generation.) Unif(0,1) PRNs can be used to generate
which of the following random entities?
a. Exp( ) random variates
b. Nor(0,1) random variates
c. Triangular random variates
d. Bern( ) random variates
e. Nonhomogeneous Poisson processes
f. All of the above --- and just about anything else!
(f).
Question 2
pts
(Lesson 7.2: Inverse Transform Theorem --- Intro.) If is an Exp( ) random variable with c.d.f.
, what's the distribution of the random variable ?
a. Unif(0,1)
b. Nor(0,1)
c. Triangular
d. Exp( )
e. None of the above
Note that , where the last step follows by the Inverse Transform
Theorem. Thus, the correct answer is (a).
Question 3
pts
(Lesson 7.2: Inverse Transform Theorem --- Intro.) If is a Unif(0,1) random variable, what's the
distribution of ?
a. Unif(0,1)
b. Nor(0,1)
, c. Triangular
d. Exp( )
e. None of the above
Since and are both Unif(0,1) (by symmetry), we have
where the last step follows from Lesson 2's Inverse Transform
Theorem example. Thus, the answer is (d).
Question 4
pts
(Lesson 7.2: Inverse Transform Theorem --- Intro.) Suppose that are i.i.d.
Unif(0,1) random variables. Using Excel (or your favorite programming language), simulate
. Draw a histogram of the 5000 numbers. What p.d.f.
does the histogram look like?
a. Uniform
b. Normal
c. Triangular
d. Exponential
e. Bernoulli
By the Inverse Transform Theorem, all of the 's are Exp( ). Since we have a histogram of 5000
of these, it really ought to look like an exponential p.d.f., , . Thus, the answer is (d).
Question 5
pts
(Lesson 7.3: Inverse Transform --- Continuous Examples.) Suppose the c.d.f. of is
, and demonstrate with .
. Then , and so . Plugging in
, we
. Thus, the correct answer is (c)
Question 6
pts
