M241 Probability Semester 011 Review Guide for 1st Test Wed., September 19th

Format of the test: Mostly problems which in a straight forward manner test your understanding of fundamental concepts covered. Some terms and formulas tested with true-false, multiple choice, or fill in the blank.

Chapter 1 Introduction

Section 1.1 Equally Likely Outcomes

Terms random experiment, outcome, outcome space, event.

Be able to calculate the probability of events where each outcome is equally likely by counting.

Section 1.3 Distributions
Set concepts: Set, subset, union, intersection, empty set, disjoint sets, complement of a set, partition

Use set notation to represent sets described in "event language" as in chart on page 19. Apply to problems.

Be able to draw Venn Diagrams representing various set combinations.

Know the 3 rules defining a probability distribution (page 21 top)

Know how to write down the probability distribution by specifying the probability of each outcome.

Use important rules of probability (see page 72 and notes) to calculate the probability of events.

1.4 Conditional Probability and Independence Know and be able to apply the general formula for conditional probability and its alternative form, the multiplication rule (top page 36-37)

Be able to set up the tree diagram for two-stage random experiments – like examples 5 and 6 and assigned problems. Use Multiplication Rule to calculate probabilities of paths.

Understand how to use the Rule of Average Conditional Probabilities (page 41)

Concept of independence of events. (See summary page 73) Know the Multiplication Rule for two Independent Events – Apply to calculating probabilities as in examples 8 and 9 and assigned exercises.

1.5 Bayes’ Rule Be able to use tree diagrams and conditional probability formulas to calculate reverse conditional probabilities as in Example 3 (false positives), Example 4 and other assigned problems 1.6 Sequences of Events Extend Multiplication Rule for more than 2 events – apply to problems like example 4, example 5 and assigned problems.

Apply Multiplication Rule for 3 or more independent events to problems like examples 6 and 7 and assigned problems
 
 

Chapter 2 Repeated Trials and Sampling

Basic principles of counting from the Appendix 1:

Addition Rule and Multiplication Rule – apply to examples

Formula for Number of orderings (permutations) of k elements from n -- apply to examples.

n!

Formula for the number of combinations of k elements from n (choosing k out of n) – binomial coefficient

Section 2.1 Binomial Distribution

Repeated Trials and Sampling

Independent Bernoulli trials -- what are they

What Binomial Distribution represents (no. of successes in n independent Bernoulli trials).

Formula for Binomial probability distribution.

Know how to calculate the Binomial coefficient (n choose k)

Section 2.2 Normal Approximation

Don’t have to memorize formula for normal curve.

What we mean informally by mean and standard deviation.

Know what the mean and standard deviation are for the Binomial distribution.

Know what the Standard Normal Cumulative Distribution Function F(z) is. For the normal distribution with mean m and variance s, how to use F (z) to calculate probabilities of an interval between a and b

Be able to use the Normal Approximation Table and properties of the normal curve (such as symmetry) to calculate probabilities.

Apply the Normal Approximation to the Binomial Distribution to problems (Like examples 1 through 4 and problems 11, 12, 13)

How to use the Normal Table and the Square Root Law to calculate confidence intervals.

What the Law of Large Numbers says.