**Announcements
Syllabus
Schedule/Downloads**

**Announcements ****(Last update: 05/07/18**)

1. 18-02-21: HW #1 assigned on 2/21 and due on 2-26

- Example 1-3: Which solution among 3 solutions is correct? Justify your answer.
- Example 2-8, 12, 14, 15, 16
- Problems 2-5, 10

2. 18-02-26: HW #2 assigned on 2/28 and due on 3/5

- Example in page 44 between the proof of the Borel-Cantelli lemma and PROBLEMS. Do not just copy but derive the result by providing details.
~~Problems 2-22 and also list all 11 equations for the independence of 4 events.~~- Solve the Monte-Hall problem with M doors, 1 BMW, and N(<M-1) doors being opened.
- Example 3-9, 10, 14
- Problem 3-5

3. 18-03-07: HW #3 assigned on 3/7 and due on 3/12

- See Wikipedia and find the definitions of quantile, quartile, decile, and percentile. Also provide some examples.

a

k-thq-quantile for a variableX

- Example 4-10, 12, 13, 16, 18, 19
- Problem 4-1, 7, 9
- Exam #1 will be taken on 3/22 from 19:30-24:00 at LG 104. Any objections?

4. 18-03-14: HW#4 assigned on 3/14 and due on 3/19

- When X is a discrete random variable and M is an event, find
- the conditional mass function,
- Total probability theorem, and
- Bayes' theorem.

- State how to invoke the Gaussian and Poisson approximations to a multi-nomial distribution.
- Examples 4-22, 29, 30, 31; 5-13, 14, 15
- Special case in p.135
- Problems 4-18, 19, 20, 21 (a posteriori = the posterior = 事後의), 33

5. 18-03-19: Exam #1 will cover upto the material of the class meeting #10.

6. 18-03-21: HW#5 assigned on 3/23 and due on 3/28

- Example 5-21, 24 (what is the unit of the variance?), 28, 32 (run length), 33
- Problems 5-25, 32, 35, 36, 37, 40, 42, 46

7. 18-03-28: HW#6 assigned on 3/28 and due on 4/2

- Examples 5-34, 35,
- State the results of Examples 6-1, 2, 3; 6, 7, 8, 9,10, 11, 12, 13, 14, 15, 16; 17, 18, 19, 20
- Q1. What are the skew and the kurtosis of a random variable?
- Q2. What is a cumulant of a random variable?
- Theorem 6-3

8. 18-04-04: HW#7 assigned on 4/4 and due on 4/9

Section 6-3

- Examples 6-22, 25
- State the results of Example 6-23, 24, 26, 27
- Problems 6-5, 18, 22, 26, 33, 48
Section 6-4

- Examples 6-31, 32,
- Problems 6-49, 52
Section 6-5

- Examples 6-34, 35, 36
- Problems 6-56, 63

9. 18-04-12: HW#8 assigned on 4/12 and due on 4/16

Sections 6-6, 7

- Examples 6-39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50,
- Problems 6-65, 73, 78, 79
Sections 7-1, 2

- Examples 7-2, 3, 5, 6, 7 (The part for E{S^2}.), 8, 9, 10,
- p. 260: Sample variance

10. 18-04-16

- On this 2nd midterm exam, there will be a problem on a mixture
distribution. For some information, see
https://en.wikipedia.org/wiki/Mixture_distribution.
- Do not see the web pages such as http://theanalysisofdata.com/probability/3_13.html that contains an incorrect information about the moments of a mixture.

11. 18-04-18: HW#9 assigned on 4/25 and due on 4/30

Section 7-3

- p. 263: Nonlinear MS Estimation, Linear MS Estimation
- pp. 270-272: Orthonormal data transformation
- Examples 7-11, 12, 13

Section 7-4

- p. 275: The law of large numbers (Bernoulli)
- p. 277: Markov's theorem

Section 7-5

- Examples 7-19, 20, 21, 22, 23, 24
- Theorem 7-3

12. 18-05-02: HW#10 assigned on 5/2 and due on 5/9

Section 9-1

- Examples 9-1, 2, 3, 4, 5, 6, 7, 8, 9; 10, 11, 12, 13, 14
- p. 391, Corollary.
- p. 393, Theorem 9-1

13. 18-05-09: HW#11 assigned on 5/9 and due on 5/14

Section 9-2

- Examples 9-15, 16, 18, 19,
- p. 401, Theorem 9-3.

14. 18-05-21: HW#12 assigned on 5/21 and due on 5/30

- Examples 9-20, 21
Section 9-3

- Examples 9-22, 23, 24, 25, 26, 27, 28, 29, 30
Section 9-4

- Examples 9-31, 32, 33, 34, 35