# Ma 405: Probability & Statistics II

Type of convergence in probability, law of large numbers, Chebyshev's inequality, central limit theory proven, development of point and interval estimates and hypothesis testing, regression, ANOVA, Chi square. Required calculator: TI 89 or Nspire CAS. Prerequisite(s): Ma 404. 3 Credits.

### Spring 2022 Course Information

- Instructor: Melissa Gardenghi
- Course Syllabus

#### Course Resources

- Project Information - Data is available in Canvas
- Modeling the Frequency and Severity by Omari et. al.
- Course Schedule for Project Planning Purposes
- Process Summary - Completion Plan Template
- Work Log Template - Copy to your Teams channel
- Current Draft - Rubric/Mathematical Evidence
- Current Draft - Rubric/Polished First Draft
- Current Draft - Rubric/Final Draft
- Current Draft - Rubric/Reflection
- Loss Models, Ch 10, 11, 14

### Tentative Course Content and Recommended Homework Problems

The tentative plan for covering course content includes the following sections (in roughly the given order). Recommended problems from the book are provided for each chapter.

Unit 1 Advanced Single Variate/Multivariate

Ch 6: Sections 3-4

# 52, 53, 60

Ch 3: Sections 5-7

# 44, 45, 97, 101, 69, 71, 73, 76, 82, 104, 105, 107 ... for #105, 107: also compute all expected values, covariances, correlations, conditional expected values, marginal expected values (and anything else you can think of)

Ch 4: Sections 6-8

# 46, 47, 49, 50, 51, 53

Ch 5: Sections 8-9

# 83, 85-87

Ch 6 Section 7

# 43, 45, 46, 48, 49

Unit 2 Functions of RVs and Sampling Distributions

Ch 7 Sections 2-5

# 1-8, 50, 51, 10-12, 16-18, 20, 22, 23, 28, 32-35, 38, 52, 59, 60, 63, 65, 67, 69, 70

Ch 8 Sections 2-7

# 46-48, 88, 52-54, 58

Unit 3 Modeling and Assessing Distributions

Simulation - see Introduction to Simulation Using R by Rakhshan and Pishro-Nik

Ch 14 Loss Models (see link in Resources) Sections 1-2

# 1-3, 7, 8a (only do mean and st dev), 9 (do mean and var instead)

Ch 13 Section 8

# 80-83

Ch 10 Sections 2-6, 7, 8

# 1, 5, 7, 11, 12, 80, 23, 24, 78, 25, 36, 37, 42-44, 78, 50, 52, 55, 84, 57, 87, 67, 88, 61, 62, 71, 92, 81, 83

Ch 11 - overview/review

Ch 12 Sections 4-6

# 1, 4, 6, 8, 31, 32, 9, 11, 12, 15, 16, 38, 20, 21, 44, 26, 39

Ch 13 Sections 6-7

Ch 15 Sections 2-3

Ch 14 Sections 1-3, 4-5

Additional problems dependent on what time allows.

## Project Resources

Anderson-Darling Test (a goodness of fit test)

Chi-Square Goodness of Fit Test

Kolmogorov-Smirnov Goodness of Fit Test