Preparing the Midterm II, STAT 3021, Fall 2011

Date: 11/23/11, Wednesday Time: 15:30 P.M. - 16:30 P.M.

1. Midterm Scope

Handout 1 Probability• Sample Space, Events.• Counting Sample Points• Probability of an Event, Conditional Probability.• Multiplicative Rules, Bayes’ Rule.

Handout 2 Random Variables and Probability Distributions• Concept of a Random Variable.• Discrete and Continuous Probability Distributions and cumulative distribu-

tion functions.• Joint Probability Distributions, Statistical Independence.

Handout 3 Mathematical Expectation• Means, Variances, Covariance, and Correlation Coefficient of Random Vari-

ables.• Means and Variances of Linear Combinations of Random Variables.• Markov’s Inequality and Chebyshev’s Theorem

Handout 4 Some Discrete Probability Distributions• Hypergeometric Distribution• Binomial and Multinomial Distributions.• Negative Binomial and Geometric Distributions.• Poisson Distribution. The Poisson Distribution as a Limiting Form of the

Binomial.Handout 5 Some Continuous Probability Distributions

• Normal Distribution and Application of Normal Distribution.• Normal Approximation to the Binomial.• Gamma, Exponential, and Chi-Squared Distributions.• Relation between the Poisson Process and the Exponential Distribution.• The Memoryless Property and Its Effect on the Exponential Dis-

tribution.Handout 6 Moments and Moment-Generating Functions

2. Midterm Preparation

• Make sure you totally understand the homework problems.• You will be allowed to use a two-page, two-sided “cheat sheets”.• You may also use standard calculators that do not have external memory drives

or data ports. However, calculators that can be used as communication devicesmay not be used.