Probability Flashcards
What is a sample space?
A sample space is a set of point, they are the possible outcomes of a trial.
What is an event
An event is a subset of a sample space
What is a probability function
And its properties
A probability is a map from events to real numbers such that
1. P(A) ≥ 0 for all events.
2. P(X) = 1
3. If A ∩ B = ∅ for two events A and B then
P(A ∪ B) = P(A) + P(B)
What is a probability mass function
And its properties
A probability mass function is a map from points in the sample space to real numbers
such that
How does a probability function relate to a probability mass function?
Calculate the probability of event A given all points in sample space have the same probability.
What is the binomial coefficient
What is the partitian function
What is conditional probability (and formula)
What is independence (formula)
What is conditional independence (formula)
What is Bayes’ rule (formula)
How does a naïve Bayes estimator work
What is a random variable
A random variable is a map from sample space to a set of numerical values
How to calculate P(X=x)
What are joint, conditional and marginal distributions?
How to calculate the expected value of a function
What is the mean
What is the varience
What is the nth moment
Properties of expected values (multiplication, addition, identity)
How to calculate varience using the 2nd moment and square of mean
What determines an event to be part of the Poisson process?
What is the Poisson distribution (and formula)
What is the distribution function
What is the density function (in relation to distribution function)
Determine distribution function from density function
Determine distribution function between 2 values
What does the Gauss/Normal distribution look like?
What is the density function for the Gauss Distribution
How to work out pobabilities of the Gauss distribution
Sum of a geometric series (and infinite) formula
Binomial distribution formula
How to derive mean and varience of binomial distribution
