## Math 375: Probability Theory Spring 2018 Exam 1 Information

Department of Mathematics and Computer Science
College of the Holy Cross

#### General Information

• The exam will be held on Tuesday, February 20, from 5:30pm to 7:00pm, in Smith Labs 154.
• Plan to arrive a few minutes early to allow time to distribute the exams.
• The exam will cover material from sections 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 3.1, 3.2, and 3.3 in the text.
• Cell-phones should be turned OFF for the duration of the exam.
• You may use a non-graphing, scientific calculator during the exam. No other calculator or electronic device may be used during the exam.
• This is a closed-book exam. No books or notes may be used during the exam.
• You will be expected to show all of your work. A correct answer with insufficient justification may not receive full credit.

#### Topics

• Sample Spaces Probabilities Be able to write the sample space for a given experiment. Know the basic axioms of probability (Def 2.6) and how to calculate probabilities of given events by the sample-point method (sum the probabilities of the sample points).
• Combinatorics Know the formulas for the number of combinations and permutations (with or without repetition) of length r from a set of n distinct objects. Also know Theorem 2.3 regarding partitions. Be able to use these results to compute probabilities of given events.
• Conditional Probability and Independence Know the definition of the conditional probability of an event A given an event B, and be able to compute it for given events A and B. Know the definition of independence of two events and be able to determine whether or not two given events are independent.
• Basic Laws of Probability Know the Multiplicative Law (Theorem 2.5), the Additive Law (Theorem 2.6), Theorem 2.7, and the Law of Total Probability (Theorem 2.8). Know how to use these laws to compute probabilities of given events (the event-composition method).
• Bayes' Rule Know how to use Bayes' Rule (Theorem 2.9) to compute given conditional probabilities.
• Random Variables Know how to find the probability distribution for a given random variable and how to use the it to find the expected value, variance, and standard deviation of the random variable.

#### Preparing for the Exam

Here are a some exercises from the text to use for practice. Solutions to most of the odd-numbered exercises are in the back of the text.

Chapter 2
Exercises 143, 146, 147, 148, 149, 150, 152, 153, 154, 155, 157, 162, 163, 164, 165, 166, 167, 170, 172, 173, 177

Chapter 3
Exercises 5, 8, 11, 13, 18, 20, 23, 24, 27, 31, 180, 185, 189