.

I will also assign homework from the textbook. This are mostly meant to check that you are following along with the class material.

The final grade will be based on HWs (10%), midterms (50%) and final (40%).

We will also discuss personal projects to be completed together with the final. To prepare a good project it is necessary to start as soon as possible. I can propose subjects for possible projects but I'd prefer if you find a problem involving differential equation you are interested in and that can be analyzed with the tools you will learn in class.

**Review: Large Samples**Law of Large Numbers, Central Limit Theorem**Basics**: Sample sets, Parametric statistical inference.**Estimstion**: Point estimation, Confidence intervals.**Estimation Techniques**: Method of Moments, Maximum Likelihood Estimation.**Asymptotic Results**: Cramer-Rao Inequality, Asymptotic normality of the MLE.**Hypothesis Testing**: Basics structure, Likelihood Ratio Tests, Chi-Squared Tests.**Applications**: Introduction to regression, Analysis of Variance**Optional (time permiotting)**: Non-parametric methods

**First and Second week.**

Material covered: Introduction and basic review of Probability Theory. Chapters 6.1, 6.2, 6.3 and 6.4.

Exercises: Chapter 6.2 ex n. 3, 7, 15, Chapter 6.3 ex n. 4, 10, Chapter 6.4 ex. n. 2.

Solution set for the first HW.

Material covered: Chapters 7.1, 7.2

Exercises: Chapter 7.2: 3, 10.

**Fourth week.**

Material covered: Chapter 7.3 with Chapters 5.7 and 5.8.

Exercises: Chapter 7.3: 7,8, 12, Chapter 5.7: 10, 19, Chapter 5.8: 5, 8

**Fifth week.**

Material covered: Chapter 7 section 7.4 and 7.5.

Exercises: Chapter 7.4: 6, 12, 13, Chapter 7.5: 5, 9, 10

Solution set for the second HW.

**Sixth and Seventh week.**

Material covered: Chapter 7 section 7.6 and 6.6 from R.V. Hoggs and E.A. Tanis "Probability ans Statistical Inference". For interested people this optional material contain a proof of consistency of the MLE estimator under mild regularity condition, from R.V. Hoggs, J.W. McKean and A.T. Craig, "Introduction to Mathematical Statistics".

Exercises: Chapter 7.6: 9, 12, 23

This is last year midterm with solution for your practice.

As quoted in the practice text, research on the relations among Pareto distribution, wealth distribution and economic inequality is active. Here a couple of example: On a Kinetic Model for a Simple Market Economy or Statistical Equilibrium Wealth Distribution in a Exchange Economy with Stochastic Preference . This is an area of research I'm quite interested in. I'll be more than happy to discuss with you if you find the question interestin

**Ninth week.**

Material covered: Chapter 8 section 8.1, 8.2 and 8.5

Exercises: Chapter 8.1: 2, 9, Chapter 8.2: 4, 7, 10, Chapter 8.5: 1, 4, 7

**Tenth week.**

Material covered: Chapter 8 section 8.3, 8.4 and 8.7

Exercises: Chapter 8.3: 5, 7 Chapter 8.4: 3, Chapter 8.5: 1, 4, 7, Chapter 8.7: 6, 11

Here is the solution set for the third HW and also last year second midterm as preparation material for the coming midterm.**Eleventh week.**

Material covered: Chapter 9 section 9.1.

Exercises: Chapter 9.1: 2, 4, 8, 10, 19

Solution set for the second midterm.