Review of probability:
a. Basic notions.
b. Random variables, Transformation of random variables, Independence.
c. Expectation, Variance, Co-variance. Conditional Expectation.

Probability inequalities: Mean estimation, Hoeffding?s inequality.

Convergence of random variables:
a. Types of convergence.
b. The law of large numbers.
c. The central limit theorem.

Statistical inference:
a. Introduction.
b. Parametric and non-parametric models.
c. Point estimation, confidence interval and hypothesis testing.

Parametric point estimation:
a. Methods for finding estimators: method of moments; maximum likelihood; other methods.
b. Properties of point estimators: bias; mean square error; consistency
c. Properties of maximum likelihood estimators.
d. Computing of maximum likelihood estimate

Parametric interval estimation
a. Introduction.
b. Pivotal Quantity.
c. Sampling from the normal distribution: confidence interval for mean, variance.
d. Large-sample confidence intervals.

Hypothesis testing concepts: parametric vs. nonparametric
a. Introduction and main definitions.
b. Sampling from the Normal distribution.
c. p-values.
d. Chi-square distribution and tests.
e. Goodness-of-fit tests.
f. Tests of independence.
g. Empirical cumulative distribution function. Kolmogorov-Smirnov Goodness-of fit test.

Regression.
a. Simple linear regression.
b. Least Squares and Maximum Likelihood.
c. Properties of least Squares estimators.
d. Prediction.