MA396 Exam I Skill Inventory
Definitions
You should be familiar with the following definitions:
- experiment
- sample outcome
- sample space
- event
- probability function
- axiom
- mutually exclusive events
- discrete probability function
- random variable
- discrete random variable
- continuous random variable
- probability density function
- cumulative distribution function
Axioms,Theorems and Applications
- Given a description of an experiment, you should be able to:
- List the elements of the sample space
- Describe the subset corresponding to a given event
- Define a probability function on the sample space assuming equally likely outcomes
- Compute the conditional probability of an event given that another event has occurred
- Given a random variable defined on the given sample space, find its expected value and variance,
and moment generating function
- Given a discrete probability density function, you should be able to:
- Find the probability that the associated random variable takes certain values
- Find its cumulative distribution function
- Find its moment generating function
- Find its mean and variance
- Given a continuous probability density function, you should be able to:
- Find the probability that the associated random variable takes values in a given interval
- Find its cumulative distribution function
- Find its moment generating function
- Find its mean and variance
- Given a continuous cumulative distribution function, you should be able to find its
associated probability density function.
- You should be familiar with the Kolmogorov axioms.
Larson and Marx Sections
The material we covered has been largely taken from the following sections of
the text. You should read these sections and attempt some of the problems.
- Section 2.3 The Probability Function
- Section 2.4 Conditional Probability
- Section 3.1 Random Variables
- Section 3.2 The Binomial and Hypergeometric Distributions
- Section 3.3 Discrete Random Variables
- Section 3.4 Continuous Random Variables
- Section 3.5 Expected Values
- Section 3.6 The Variance
- Section 3.12 Moment Generating Functions