Exercise
6
Point Estimation
Deadline: November 2, 2016.
1. Reading.
(a) Lecture notes 6
(b) Chapter 7 of the book Statistical Inference.
2. Let X be an observation from the pdf
f (x|) = ( )|x| (1 )1|x| ,
2
x = 1, 0, 1;
01
(a) Find the MLE of
(b) Define t

Exercise
2
Random Variables
Deadline: October 7, 2016.
1. Reading.
(a) Lecture notes 2
(b) Chpaters 2 and 3 of the book Statistical Inference.
2. In each of the following show that the given function is a cdf and find
FX1 (y).
(
(a) FX (x) =
0
if x < 0
x

Exercise
3
Random Vectors
Deadline: October 12, 2016.
1. Reading.
(a) Lecture notes 3
(b) Chpater 4 of the book Statistical Inference.
2. The joint distribution of X and Y is
2
cx y,
f (x, y) =
0,
x2 y 1
other
(a) Calculate the constant c.
(b) Find the m

Exercise
7
Mixture Models
Deadline: December 4, 2016.
Background
de novo motif finding is a classical problem that can be addressed by using a mixture model.
Particularly, the one motif per sequence problem can be simplified as follows.
There are a total

Exercise
5
Principles of Data Reduction
Deadline: October 26, 2016.
1. Reading.
(a) Lecture notes 5
(b) Chapter 6 and chapter 7.1, 7.2 of the book Statistical Inference.
2. Let X1 , . . . , Xn be a random sample of size n from a Gamma(shape =
, scale = )

Exercise
4
Random Sampling
Deadline: October 19, 2016.
Note:
For calculation problem, please give details of the derivation. Answers will
receive only half of the points.
1. Reading.
(a) Lecture notes 4.
(b) Chapter 5 of the book Statistical Inference.
2.

Exercise
1
Probability Theory
Deadline: September 28, 2016.
Note:
For calculation problem, please give details of the derivation. Answers will
receive only half of the points.
1. Reading.
(a) Lecture notes 1.
(b) Chapter 1 of the book Statistical Inferenc