STAT 5361 Homework 4
Due at May 4.
1.
Suppose X has the folling probability density function
1
f (x) = p x2 e
2 2
(x 2)2
2
1 < x < 1.
,
Consider using the importance sampling method to estimate E(X).
a) Implement the important sampling method, with g(x) b
Homework 1. Due Thursday, February 20.
Note. Collaborations are allowed for this homework. Each group can have at most 2 students.
No collaborations between groups are allowed.
1.
The Cauchy(, 1) distribution has probability density
p(x ) =
1
.
[1 + (x )2
Homework 2. Due Thursday, March 13.
Note. Collaborations are allowed for this homework. Each group can have at most 2 students.
No collaborations between groups are allowed.
1.
Let f and g be two probability densities on (0, ), such that
f (x) 4 + x x1 ex
Homework 3. Due Thursday, April 10
For each question, in addition to computer code, mathematical derivations must be
provided as the rationale for the code.
1.
Use the random walk construction to simulate the Brownian motion
dX(t) = (a cos t) dt +
1
dW (t
STAT 5361 Final Exam
Due at Noon, Wednesday, May 7.
Note. This is a take-home exam. Students can form groups to work on the exam. The number of
students in each group must not exceed 2. No collaborations between groups are allowed.
1.
Suppose X and Y have
1
0.1. LIKELIHOOD RATIO TESTS
0.1
Likelihood Ratio Tests
Likelihood ratio tests are a very general approach to testing.
Let f (x; ) be either a probability density function or a probability distribution where is a real valued parameter taking values in an